REVIEW 3 major objections 4 minor 180 references
On Non-Stationary Dynamic Pricing: Adaptivity and Optimality
T0 review · 3 major / 4 minor · reviewed 2026-07-31 · deepseek-v4-flash
Pith's one-line read This paper claims that a single algorithm, MCP-DP, achieves minimax-optimal regret in non-stationary contextual dynamic pricing without knowing whether demand changes abruptly or smoothly, and proves a matching dimension-dependent lower bou
desk verdict If the missing supplement holds up, this closes the adaptivity gap in non-stationary contextual dynamic pricing; right now the main theorems are unverifiable because every load-bearing lemma is in that supplement. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is the multiscale likelihood-ratio change-point test. Within each epoch, the horizon is split into dyadic blocks; a scheduler randomly samples exploration intervals of many different lengths, and on each such interval the algorithm compares the current reference model's negative log-likelihood with that of the best GLM fit. The key identity (Corollary 3.1) is that the likelihood-ratio statistic is sandwiched between two multiples of the design-adjusted prediction error of the reference model, up to statistical noise and non-stationarity bias. Because shorter intervals are sampled more often than longer ones, any interval carrying excessive regret is likely to contain
What would settle it
Run MCP-DP on a single linear-demand instance with smooth drift of known budget V_T and no change-points, and measure the regret's growth in T; the claimed theorem says it scales as V_T^{1/3} T^{2/3} up to logarithmic factors. If the observed growth is closer to T, or if the constant degrades with d faster than d^{1/3}, the upper bound fails. Conversely, for a two-segment instance with d=2 and large T, compute the minimax regret over all non-anticipating policies; if any policy beats c sqrt(s d T) polylog for all large T, the lower bound fails.
Extended reading notes
Core claim
The paper's central claim is that adaptivity to the nature of non-stationarity is achievable in contextual dynamic pricing: a single policy, MCP-DP, attains regret of order sqrt(s_T d T) ∧ {sqrt(dT) + V_T^{1/3} d^{1/3} T^{2/3}} up to log factors, with no knowledge of the segment count s_T or the variation budget V_T, and this rate is minimax optimal. The argument rests on a new prediction-error bound for maximum likelihood estimators fit to a mixture of generalized linear models, and on a multiscale change-point detection scheme whose likelihood-ratio statistic is provably a surrogate for the unobserved exploitation regret. The paper also constructs the first minimax lower bound for this pro
Load-bearing premise
The contexts must be independent draws from a fixed distribution whose covariance has full rank; if contexts are adversarial or nearly collinear, the regret guarantee does not hold (and the paper says removing this would require a different method).
Editorial extensions
If this is right
- A seller can run a single pricing policy across markets that experience holiday demand spikes and markets that drift slowly with inflation, and pay (up to logs) only the better of the two tailored costs.
- The dimension d enters both terms of the bound (sqrt(d) or d^{1/3}), so the lower bound makes precise that high-dimensional contexts are intrinsically harder in non-stationary pricing, not just in estimation.
- The design-adjusted variation budget means changes in parameter directions that the context distribution rarely visits are nearly free; only changes that actually move the demand distribution hurt revenue.
- The MLE prediction-error bound for mixtures of GLMs is a standalone statement that can be reused in other online decision problems with drifting GLM structure.
- Because the bound does not require identifying every change-point, the algorithm stays valid under frequent small changes where exact localization is impossible.
Reading between the lines
- The same multiscale LRT scheme is a plausible template for non-stationary contextual bandits with continuous actions and varying contexts, a regime the paper notes existing adaptive bandit reductions exclude; this extension is the authors' own conjecture and untested here.
- One testable practical prediction is that recording the context covariance is enough to decide which coefficient shifts matter: two environments with the same L2 variation can have very different regrets if one varies along low-density directions, and the design-adjusted budget explains exactly that.
- If the stochastic-context assumption were relaxed to adversarial contexts, the restart-triggering signal would degrade; the paper itself concedes this needs fundamentally different methods, suggesting a real frontier for future work.
- The multiple-classification lower-bound construction may transfer to other continuous-action non-stationary problems, such as dynamic assortment or personalized recommendations, giving dimension-dependent limits in those settings as well.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper studies non-stationary contextual dynamic pricing with a GLM demand model and stochastic contexts. It introduces a design-adjusted variation budget V_T, proposes the MCP-DP algorithm (multiscale likelihood-ratio change-point detection with localized exploration), and claims a regret bound of order Õ(sqrt(s_T d T) ∧ {sqrt(dT) + d^{1/3} V_T^{1/3} T^{2/3}}) without knowing s_T or V_T (Theorem 3.1). A matching minimax lower bound is stated in Theorem 2.1 using a new Assouad-based construction. The paper also reports extensive numerical experiments comparing MCP-DP with the non-adaptive CPDP and MWDP baselines.
Significance. If the proofs are valid, this is a substantial contribution: it would be the first contextual dynamic-pricing algorithm that is adaptive to both piecewise-stationary and smoothly varying environments, with dimension-aware rates and a new sharp notion of variation budget. The algorithm design is interesting, and the experiments support the claimed adaptivity. The paper also ships explicit algorithm pseudocode, theorem statements with concrete threshold laws, and a detailed proof sketch. However, all load-bearing proof components are deferred to a supplement that is not included in the arXiv submission, so the central claims cannot currently be certified.
major comments (3)
- [§3.3 / Supplement S.2–S.4] The proof of Theorem 3.1 rests on Proposition 3.1, Corollary 3.1, and Lemmas S.4.1–S.4.6, whose proofs are all in the Supplementary Material. These are not peripheral: Corollary 3.1 is what makes the LRT statistic a surrogate for the unobserved exploitation regret, Lemma S.4.5 supplies the dyadic-scale covering argument that guarantees a suitably scaled exploration window triggers a restart, and Lemma S.4.6 controls the regret before a missed detection is caught. The sketch states that constants must satisfy c_4^*−c_3^*>c_γ and that intervals must satisfy |J|≥32c_z²(κλ_z)^{-1}log(dT), but those facts are exactly what needs proof. As submitted, the central upper bound is not verifiable. Please include the full supplement.
- [§2.4, Theorem 2.1] The theorem is stated for T≳s d log(dT) ∧ d V log^{3/2}(dT). For the lower bound to cover the √(s d T) regime, one typically needs T to be at least on the order of s d log(dT), and for the variation regime one needs T to be at least d V log^{3/2}(dT); the condition should therefore be a conjunction (equivalently, use ∨ or the requirement that T is at least both). With the current ∧, if s is large but V is small, the condition can hold while T≪s d log(dT), making the claimed √(s d T) lower bound unsupported. Please correct or justify the condition.
- [§2.4 / Supplement S.2] The minimax lower bound is announced in Theorem 2.1 but the proof is described only at a high level and deferred entirely to Section S.2, which is not present in the submitted files. Since the claimed novelty includes a 2^d-sized hard instance and an Assouad argument with diverging d, the lower-bound proof is a load-bearing part of the paper's central claim. It must be included in the review package so that the construction, the two-hypothesis separation, and the reduction from regret to classification error can be checked.
minor comments (4)
- [§3.2, Eq. (14)] The constant c_1^* in the last inequality is not defined, and the first equivalence (regret ≍ squared price difference) should state explicitly which constants from Assumptions 2.2–2.3 it depends on. Please make the display self-contained.
- [Algorithm 1, line 16] The mandatory block-end exploration interval E_{i,j} = [τ_i+2^jL−ℓ_j+1, τ_i+2^jL] should be intersected with the block B_{i,j}, as is done for J_{i,j}(s,m). Without this, the interval can start before the block for small j, depending on the precise definition of ℓ_j.
- [§4.1] The recommended threshold γ=d(log(Td))^{1.1} is not literally the theoretical γ=c_γ d log(dT). Since the theorem requires c_γ sufficiently large, please state how large Td must be so that (log(Td))^{0.1} dominates the required c_γ.
- [§2.2, Definition 2.2] The definition of P_I as 'ordered partitions' is clear in spirit, but the notation would benefit from explicitly saying that {t_0,...,t_m} is a grid with I_a=t_0<...<t_m=I_b and that m ranges over all positive integers; the current wording 'for some m=1,2,...,I_b−I_a' is slightly off when I_a=1 and I_b=T because the number of segments is m.
Circularity Check
No circularity: the upper and lower bounds are independent constructions, the algorithm is parameter-free with respect to s_T and V_T, and the main regret claim does not reduce to a fitted input or a self-citation chain.
full rationale
I found no step in which a claimed prediction is equivalent by construction to an input, nor any fitted parameter renamed as a prediction. Definitions 2.1 and 2.2 define s_T and V_T as environment parameters before any theorem, and the MCP-DP algorithm is not told their values. The LRT statistic in (10) is not declared equal to regret by definition; Corollary 3.1 is a substantive two-sided inequality relating Lambda_J to design-adjusted prediction error and V_J, and the proof, although deferred to the supplement, is a mathematical argument rather than a definitional tautology. Likewise, (14) uses a Taylor expansion and Lipschitz property of the optimal price, not a re-use of the regret being bounded. The tuning parameters c_L and c_gamma are universal constants with the theorem stated for sufficiently large values, so no data-dependent fitting is performed; the practical threshold recommendation gamma = d{log(Td)}^{1.1} is not used to derive Theorem 3.1. The minimax lower bound in Theorem 2.1 is based on a separate Assouad hard-instance construction and does not reuse the upper-bound proof, and the two bounds are not derived from each other. The paper does cite prior work by the same authors, notably Zhao et al. (2026a) for a Lipschitz property of the optimal price and Zhao et al. (2026b) for benchmarks and context-free lower bounds, but these citations are standard, parameter-free supporting facts rather than a load-bearing uniqueness or ansatz chain. I also flag, per the reviewing rule, that Proposition 3.1, Corollary 3.1, and Lemmas S.4.5/S.4.6 are proved only in Sections S.2-S.4 of the Supplement, which are not included in the provided manuscript, so the formal correctness of the central claim cannot be fully certified from the submitted text. This is a verification gap, not evidence of circularity. The Section 5 limitation that relaxing the stochastic-context assumption 'would require fundamentally different upper bound algorithms' similarly weakens the scope but does not make the derivation circular. Overall circularity score: 0.
Assumptions & free parameters
free parameters (1)
- Algorithm tuning constants c_L, c_γ (and exploration deviation ρ) =
c_L=2 and γ=d{log(dT)}^{1.1} in experiments; theory requires sufficiently large c_L,c_γ
assumptions (5)
- domain assumption Canonical GLM with known ψ, scale a(ϕ), normalizer h(y), and E[y|x,θ]=ψ'(x^T θ)
- domain assumption Assumption 2.1: contexts {z_t} i.i.d. on a compact set with full-rank covariance Σ_z
- domain assumption Assumption 2.2: sub-Gaussian demand noise; ψ ∈ C^3 with ψ'' > 0
- domain assumption Assumption 2.3: bounded convex parameter space; bounded z^T α and z^T β; unique interior optimal price
- standard math Standard concentration inequalities (Bernstein, Hoeffding, matrix Chernoff)
invented entities (1)
-
Design-adjusted variation budget V_T (Definition 2.2)
Cite this review
Pith. "Pith review of On Non-Stationary Dynamic Pricing: Adaptivity and Optimality." pith.science (2026). https://pith.science/paper/FPSVCLUT
@misc{pith2026260724115,
author = {Pith},
title = {Pith review of: On Non-Stationary Dynamic Pricing: Adaptivity and Optimality},
year = {2026},
howpublished = {\url{https://pith.science/paper/FPSVCLUT}},
note = {Machine review of arXiv:2607.24115}
}
abstract
We study the contextual dynamic pricing problem under non-stationarity, where a firm sells products to $T$ sequentially arriving consumers that behave according to an unknown demand model that can change over time. The demand model is assumed to be a generalized linear model (GLM), allowing for a feature vector in $\mathbb{R}^d$ that encodes products and consumer information. To achieve optimal revenue (i.e., least regret), the firm needs to learn and exploit the unknown GLMs while monitoring for potential changes. We propose a multiscale change-point detection based algorithm that achieves a regret of order $\widetilde{O}(\sqrt{s_TdT}\wedge\{V_T^{1/3}d^{1/3}T^{2/3}+\sqrt{dT}\})$, where $s_T$ is the number of piecewise stationary segments and $V_T$ is a newly defined notion of design-adjusted variation budget of model parameters. Our algorithm is adaptive and does not require knowing $s_T$ or $V_T$. Moreover, to our knowledge, this is the first dynamic pricing algorithm that is adaptive to the nature of changes and achieves the best-of-both-worlds rate, thus closing a long-standing gap in the literature. We remark that, due to the varying contexts, existing works in the adaptive non-stationary bandit literature cannot be applied to achieve optimality for contextual dynamic pricing. The regret is further accompanied with a newly constructed minimax lower bound, confirming the optimality of our algorithm (up to logarithmic factors). Extensive numerical experiments are conducted to illustrate the efficiency and robustness of the proposed algorithm in non-stationary dynamic pricing.
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Reference graph
Works this paper leans on
-
[1]
1998 , publisher=
Mathematical statistics , author=. 1998 , publisher=
1998
-
[2]
Operations Research , volume=
Online decision making with high-dimensional covariates , author=. Operations Research , volume=. 2020 , publisher=
2020
-
[3]
Wild binary segmentation for multiple change-point detection , author=
-
[4]
A Turning Point for Private Brands: How Retailers Can Seize the Opportunity , year =
McOuat, Angus and Kuijpers, Dymfke and. A Turning Point for Private Brands: How Retailers Can Seize the Opportunity , year =
-
[5]
Operations Research , volume=
On dynamic pricing with covariates , author=. Operations Research , volume=. 2025 , publisher=
2025
-
[6]
The Review of Asset Pricing Studies , volume=
How does household spending respond to an epidemic? Consumption during the 2020 COVID-19 pandemic , author=. The Review of Asset Pricing Studies , volume=. 2020 , publisher=
2020
-
[7]
Marketing Letters , volume=
Price elasticity dynamics over the product life cycle: A study of consumer durables , author=. Marketing Letters , volume=. 1997 , publisher=
1997
-
[8]
Conference on learning theory , pages=
Non-stationary reinforcement learning without prior knowledge: An optimal black-box approach , author=. Conference on learning theory , pages=. 2021 , organization=
2021
Show all 180 references
-
[9]
arXiv preprint arXiv:2406.13197 , year=
Representation transfer learning for semiparametric regression , author=. arXiv preprint arXiv:2406.13197 , year=
-
[10]
arXiv preprint arXiv:2303.17765 , year=
Learning from similar linear representations: Adaptivity, minimaxity, and robustness , author=. arXiv preprint arXiv:2303.17765 , year=
-
[11]
2013 , publisher=
Matrix Analysis , author=. 2013 , publisher=
2013
-
[12]
International Conference on Machine Learning , pages=
Pricing experimental design: causal effect, expected revenue and tail risk , author=. International Conference on Machine Learning , pages=. 2023 , organization=
2023
-
[14]
arXiv preprint arXiv:2302.10160 , year=
Pseudo-labeling for kernel ridge regression under covariate shift , author=. arXiv preprint arXiv:2302.10160 , year=
-
[15]
Foundations and Trends
An introduction to matrix concentration inequalities , author=. Foundations and Trends. 2015 , publisher=
2015
-
[16]
Management Science , volume=
Personalized dynamic pricing with machine learning: High-dimensional features and heterogeneous elasticity , author=. Management Science , volume=. 2021 , publisher=
2021
-
[17]
arXiv preprint arXiv:2205.03880 , year=
Optimal change-point testing for high-dimensional linear models with temporal dependence , author=. arXiv preprint arXiv:2205.03880 , year=
-
[18]
Journal of Machine Learning Research , volume=
Statistically and computationally efficient change point localization in regression settings , author=. Journal of Machine Learning Research , volume=. 2021 , publisher=
2021
-
[19]
A tail inequality for quadratic forms of subgaussian random vectors , author=
-
[20]
International Conference on Machine Learning , pages=
Provably optimal algorithms for generalized linear contextual bandits , author=. International Conference on Machine Learning , pages=. 2017 , organization=
2017
-
[21]
Operations Research , year=
On adaptivity in nonstationary stochastic optimization with bandit feedback , author=. Operations Research , year=
-
[22]
, author=
An Efficient Two Step Algorithm for High Dimensional Change Point Regression Models Without Grid Search. , author=. Journal of Machine Learning Research , volume=
-
[23]
Least angle regression , author=
-
[24]
Electronic Journal of Statistics , volume=
Regret lower bound and optimal algorithm for high-dimensional contextual linear bandit , author=. Electronic Journal of Statistics , volume=. 2021 , publisher=
2021
-
[25]
Journal of the Royal Statistical Society: Series B: Statistical Methodology , volume=
The lasso for high dimensional regression with a possible change point , author=. Journal of the Royal Statistical Society: Series B: Statistical Methodology , volume=
-
[26]
Algorithmic Learning Theory , pages=
Sequential change-point detection: Laplace concentration of scan statistics and non-asymptotic delay bounds , author=. Algorithmic Learning Theory , pages=. 2019 , organization=
2019
-
[27]
Journal of Machine Learning Research , volume=
Sequential change-point detection in high-dimensional Gaussian graphical models , author=. Journal of Machine Learning Research , volume=. 2020 , publisher=
2020
-
[28]
Communications in Statistics-Simulation and Computation , volume=
Bootstrap procedures for online monitoring of changes in autoregressive models , author=. Communications in Statistics-Simulation and Computation , volume=. 2016 , publisher=
2016
-
[29]
Journal of Time Series Analysis , volume=
A new approach for open-end sequential change point monitoring , author=. Journal of Time Series Analysis , volume=. 2021 , publisher=
2021
-
[30]
2018 52nd Asilomar Conference on Signals, Systems, and Computers , pages=
Sequential graph scanning statistic for change-point detection , author=. 2018 52nd Asilomar Conference on Signals, Systems, and Computers , pages=. 2018 , organization=
2018
-
[31]
Journal of the Royal Statistical Society: Series B: Statistical Methodology , volume=
On-line inference for multiple changepoint problems , author=. Journal of the Royal Statistical Society: Series B: Statistical Methodology , volume=. 2007 , publisher=
2007
-
[32]
Annals of Statistics , volume=
Sequential change-point detection based on nearest neighbors , author=. Annals of Statistics , volume=. 2019 , publisher=
2019
-
[33]
arXiv preprint arXiv:2003.03668 , year=
High-dimensional, multiscale online changepoint detection , author=. arXiv preprint arXiv:2003.03668 , year=
2003 arXiv
-
[34]
arXiv preprint arXiv:2101.05477 , year=
Optimal network online change point localisation , author=. arXiv preprint arXiv:2101.05477 , year=
-
[35]
Advances in Neural Information Processing Systems , volume=
Locally private online change point detection , author=. Advances in Neural Information Processing Systems , volume=
-
[36]
arXiv preprint arXiv:2110.06450 , year=
Online network change point detection with missing values , author=. arXiv preprint arXiv:2110.06450 , year=
-
[37]
arXiv preprint arXiv:2006.03283 , year=
A note on online change point detection , author=. arXiv preprint arXiv:2006.03283 , year=
2006 arXiv
-
[38]
Journal of Machine Learning Research , volume=
Restricted eigenvalue properties for correlated Gaussian designs , author=. Journal of Machine Learning Research , volume=. 2010 , publisher=
2010
-
[39]
Statistical Science , volume=
A unified framework for high-dimensional analysis of M -estimators with decomposable regularizers , author=. Statistical Science , volume=. 2012 , publisher=
2012
-
[40]
Journal of Machine Learning Research , volume=
Dynamic pricing in high-dimensions , author=. Journal of Machine Learning Research , volume=
-
[41]
NSF-CBMS Regional Conference Series in Probability and Statistics, 2
Empirical Processes: Theory and Applications , author=. NSF-CBMS Regional Conference Series in Probability and Statistics, 2. Institute of Mathematical Statistics, Hayward, CA; American Statistical Association, Alexandria, VA , year=
-
[42]
Journal of the American Statistical Association , number=
Transfer learning under high-dimensional generalized linear models , author=. Journal of the American Statistical Association , number=. 2022 , publisher=
2022
-
[43]
Operations Research , volume=
Dynamic pricing under a general parametric choice model , author=. Operations Research , volume=. 2012 , publisher=
2012
-
[44]
Operations Research , volume=
On the minimax complexity of pricing in a changing environment , author=. Operations Research , volume=. 2011 , publisher=
2011
-
[45]
2009 , publisher=
Introduction to Nonparametric Estimation , author=. 2009 , publisher=
2009
-
[46]
Mathematics of Operations Research , volume=
Chasing demand: Learning and earning in a changing environment , author=. Mathematics of Operations Research , volume=. 2017 , publisher=
2017
-
[47]
2019 , publisher=
High-Dimensional Statistics: A Non-Asymptotic Viewpoint , author=. 2019 , publisher=
2019
-
[48]
Conference on Learning Theory , pages=
Reconstruction from anisotropic random measurements , author=. Conference on Learning Theory , pages=. 2012 , organization=
2012
-
[49]
International Conference on Algorithmic Learning Theory , pages=
On upper-confidence bound policies for switching bandit problems , author=. International Conference on Algorithmic Learning Theory , pages=. 2011 , organization=
2011
-
[50]
Management Science , volume=
The effectiveness of field price discretion: Empirical evidence from auto lending , author=. Management Science , volume=. 2015 , publisher=
2015
-
[51]
Management Science , volume=
Meta dynamic pricing: Transfer learning across experiments , author=. Management Science , volume=. 2022 , publisher=
2022
-
[52]
arXiv preprint arXiv:2109.07340 , year=
Distribution-free contextual dynamic pricing , author=. arXiv preprint arXiv:2109.07340 , year=
-
[53]
Journal of Applied Econometrics , volume=
Computation and analysis of multiple structural change models , author=. Journal of Applied Econometrics , volume=. 2003 , publisher=
2003
-
[54]
2015 , publisher=
Foundations of Linear and Generalized Linear Models , author=. 2015 , publisher=
2015
-
[55]
Proceedings of the National Academy of Sciences , volume=
Two theorems in graph theory , author=. Proceedings of the National Academy of Sciences , volume=. 1957 , publisher=
1957
-
[56]
Management Science , volume=
Privacy-preserving dynamic personalized pricing with demand learning , author=. Management Science , volume=. 2022 , publisher=
2022
-
[57]
arXiv preprint arXiv:1604.07463 , year=
Dynamic pricing with demand covariates , author=. arXiv preprint arXiv:1604.07463 , year=
-
[58]
International Conference on Artificial Intelligence and Statistics , pages=
A single algorithm for both restless and rested rotting bandits , author=. International Conference on Artificial Intelligence and Statistics , pages=. 2020 , organization=
2020
-
[59]
Chen, Yiwei and Wen, Zheng and Xie, Yao , journal=
-
[60]
Journal of Machine Learning Research , volume=
Efficient Change-Point Detection for Tackling Piecewise-Stationary Bandits , author=. Journal of Machine Learning Research , volume=
-
[61]
How the semiconductor industry can emerge stronger after the
Bauer, Harald and Burkacky, Ondrej and Kenevan, Peter and Mahindroo, Abhijit and Patel, Mark , year=. How the semiconductor industry can emerge stronger after the
-
[62]
2020 , journal=
What people are buying as they heed coronavirus stay-at-home orders , author=. 2020 , journal=
2020
-
[63]
2020 , journal=
24 things that have been selling out online during the coronavirus pandemic , author=. 2020 , journal=
2020
-
[64]
Management Science , volume=
Hedging the drift: Learning to optimize under nonstationarity , author=. Management Science , volume=. 2022 , publisher=
2022
-
[65]
The 22nd International Conference on Artificial Intelligence and Statistics , pages=
Learning to optimize under non-stationarity , author=. The 22nd International Conference on Artificial Intelligence and Statistics , pages=. 2019 , organization=
2019
-
[66]
Journal of the Royal Statistical Society: Series B: Statistical Methodology , volume=
Regression shrinkage and selection via the lasso , author=. Journal of the Royal Statistical Society: Series B: Statistical Methodology , volume=. 1996 , publisher=
1996
-
[67]
Sequential Analysis , volume=
Sequential change-point detection when the pre-and post-change parameters are unknown , author=. Sequential Analysis , volume=. 2010 , publisher=
2010
-
[69]
2011 , publisher=
Statistics for High-Dimensional Data: Methods, Theory and Applications , author=. 2011 , publisher=
2011
-
[70]
arXiv preprint arXiv:2205.12431 , year=
Detecting Abrupt Changes in Sequential Pairwise Comparison Data , author=. arXiv preprint arXiv:2205.12431 , year=
-
[71]
arXiv preprint arXiv:1601.03704 , year=
Computationally efficient change point detection for high-dimensional regression , author=. arXiv preprint arXiv:1601.03704 , year=
-
[72]
arXiv preprint arXiv:2006.03572 , year=
Detecting abrupt changes in high-dimensional self-exciting Poisson processes , author=. arXiv preprint arXiv:2006.03572 , year=
2006 arXiv
-
[73]
arXiv preprint arXiv:2207.12453 , year=
Change point inference in high-dimensional regression models under temporal dependence , author=. arXiv preprint arXiv:2207.12453 , year=
-
[74]
International Conference on Artificial Intelligence and Statistics , pages=
Localizing changes in high-dimensional regression models , author=. International Conference on Artificial Intelligence and Statistics , pages=. 2021 , organization=
2021
-
[75]
Operations Research , volume=
Dynamic pricing for nonperishable products with demand learning , author=. Operations Research , volume=. 2009 , publisher=
2009
-
[76]
Operations Research , volume=
Dynamic pricing without knowing the demand function: Risk bounds and near-optimal algorithms , author=. Operations Research , volume=. 2009 , publisher=
2009
-
[77]
Operations Research , volume=
Blind network revenue management , author=. Operations Research , volume=. 2012 , publisher=
2012
-
[78]
Management Science , volume=
Welfare analysis of dynamic pricing , author=. Management Science , volume=. 2019 , publisher=
2019
-
[79]
Available at SSRN 3456834 , year=
Tailored base-surge policies in dual-sourcing inventory systems with demand learning , author=. Available at SSRN 3456834 , year=
-
[80]
Operations Research , volume=
Dynamic pricing and demand learning with limited price experimentation , author=. Operations Research , volume=. 2017 , publisher=
2017
-
[81]
Operations Research , volume=
Dynamic pricing and learning with finite inventories , author=. Operations Research , volume=. 2015 , publisher=
2015
-
[82]
Operations Research , volume=
Dynamic pricing with a prior on market response , author=. Operations Research , volume=. 2010 , publisher=
2010
-
[83]
Operations Research , volume=
Online network revenue management using thompson sampling , author=. Operations Research , volume=. 2018 , publisher=
2018
-
[84]
Management Science , volume=
Bayesian dynamic pricing policies: Learning and earning under a binary prior distribution , author=. Management Science , volume=. 2012 , publisher=
2012
-
[85]
Operations Research , volume=
Dynamic pricing with an unknown demand model: Asymptotically optimal semi-myopic policies , author=. Operations Research , volume=. 2014 , publisher=
2014
-
[86]
Management Science , volume=
Multimodal dynamic pricing , author=. Management Science , volume=. 2021 , publisher=
2021
-
[87]
Management Science , volume=
Data-driven dynamic pricing and ordering with perishable inventory in a changing environment , author=. Management Science , volume=. 2022 , publisher=
2022
-
[88]
1985 , publisher=
Sequential analysis: tests and confidence intervals , author=. 1985 , publisher=
1985
-
[89]
1993 , publisher=
Nonparametric Methods in Change Point Problems , author=. 1993 , publisher=
1993
-
[90]
Journal of the Royal Statistical Society: Series B: Statistical Methodology , volume=
Sequential changepoint detection in quality control and dynamical systems , author=. Journal of the Royal Statistical Society: Series B: Statistical Methodology , volume=. 1995 , publisher=
1995
-
[91]
IEEE Transactions on Information Theory , volume=
Information bounds and quick detection of parameter changes in stochastic systems , author=. IEEE Transactions on Information Theory , volume=. 1998 , publisher=
1998
-
[92]
2012 , publisher=
Parametric Statistical Change Point Analysis , author=. 2012 , publisher=
2012
-
[93]
2014 , publisher=
Sequential Analysis: Hypothesis Testing and Change point Detection , author=. 2014 , publisher=
2014
-
[94]
Wiley Interdisciplinary Reviews: Computational Statistics , volume=
A survey of numerical algorithms that can solve the Lasso problems , author=. Wiley Interdisciplinary Reviews: Computational Statistics , volume=. 2023 , publisher=
2023
-
[95]
Journal of Statistical Software , volume=
Regularization paths for generalized linear models via coordinate descent , author=. Journal of Statistical Software , volume=. 2010 , publisher=
2010
-
[96]
SIAM Journal on Computing , volume=
The nonstochastic multiarmed bandit problem , author=. SIAM Journal on Computing , volume=. 2002 , publisher=
2002
-
[97]
Machine Learning: ECML 2006: 17th European Conference on Machine Learning Berlin, Germany, September 18-22, 2006 Proceedings 17 , pages=
Bandit based monte-carlo planning , author=. Machine Learning: ECML 2006: 17th European Conference on Machine Learning Berlin, Germany, September 18-22, 2006 Proceedings 17 , pages=. 2006 , organization=
2006
-
[98]
Advances in Neural Information Processing Systems , volume=
Stochastic multi-armed-bandit problem with non-stationary rewards , author=. Advances in Neural Information Processing Systems , volume=
-
[99]
Proceedings of the AAAI Conference on Artificial Intelligence , volume=
A change-detection based framework for piecewise-stationary multi-armed bandit problem , author=. Proceedings of the AAAI Conference on Artificial Intelligence , volume=
-
[100]
Operations Research , year=
Differential privacy in personalized pricing with nonparametric demand models , author=. Operations Research , year=
-
[101]
Journal of Machine Learning Research , volume=
Dynamic assortment optimization with changing contextual information , author=. Journal of Machine Learning Research , volume=. 2020 , publisher=
2020
-
[102]
Journal of the American Statistical Association , volume=
Structural break estimation for nonstationary time series models , author=. Journal of the American Statistical Association , volume=. 2006 , publisher=
2006
-
[103]
Management Science , volume=
Dynamic learning and pricing with model misspecification , author=. Management Science , volume=. 2019 , publisher=
2019
-
[104]
Operations Research, in press , year=
Online learning and pricing for service systems with reusable resources , author=. Operations Research, in press , year=
-
[105]
Available at SSRN 4349904 , year=
Online Learning and Pricing for Multiple Products with Reference Price Effects , author=. Available at SSRN 4349904 , year=
-
[106]
Journal of the American Statistical Association , volume=
Joint structural break detection and parameter estimation in high-dimensional nonstationary VAR models , author=. Journal of the American Statistical Association , volume=. 2022 , publisher=
2022
-
[107]
Operations Research , volume=
Nonparametric pricing analytics with customer covariates , author=. Operations Research , volume=. 2021 , publisher=
2021
-
[108]
Operations Research, forthcoming , year=
Selling quality-differentiated products in a Markovian market with unknown transition probabilities , author=. Operations Research, forthcoming , year=
-
[109]
Available at SSRN 3686518 , year=
Data-driven clustering and feature-based retail electricity pricing with smart meters , author=. Available at SSRN 3686518 , year=
-
[110]
Operations Research , volume=
Dynamic learning and market making in spread betting markets with informed bettors , author=. Operations Research , volume=. 2021 , publisher=
2021
-
[111]
Operations Research, forthcoming , year=
Markdown policies for demand learning with forward-looking customers , author=. Operations Research, forthcoming , year=
-
[112]
Management Science , volume=
Dynamic pricing with demand learning and reference effects , author=. Management Science , volume=. 2022 , publisher=
2022
-
[113]
Advances in Neural Information Processing Systems , volume=
Optimal best-arm identification in linear bandits , author=. Advances in Neural Information Processing Systems , volume=
-
[114]
arXiv preprint arXiv:2602.10483 , year=
Pricing Query Complexity of Multiplicative Revenue Approximation , author=. arXiv preprint arXiv:2602.10483 , year=
-
[115]
Management Science , year=
Dynamic batch learning in high-dimensional sparse linear contextual bandits , author=. Management Science , year=
-
[116]
arXiv preprint arXiv:2004.06321 , year=
Sequential batch learning in finite-action linear contextual bandits , author=. arXiv preprint arXiv:2004.06321 , year=
2004 arXiv
-
[117]
International Conference on Machine Learning , pages=
Sparsity-agnostic lasso bandit , author=. International Conference on Machine Learning , pages=. 2021 , organization=
2021
-
[118]
Advances in Neural Information Processing Systems , volume=
Doubly-robust lasso bandit , author=. Advances in Neural Information Processing Systems , volume=
-
[119]
Artificial Intelligence and Statistics , pages=
Online-to-confidence-set conversions and application to sparse stochastic bandits , author=. Artificial Intelligence and Statistics , pages=. 2012 , organization=
2012
-
[120]
Advances in neural information processing systems , volume=
Improved algorithms for linear stochastic bandits , author=. Advances in neural information processing systems , volume=
-
[121]
2017 International Conference on Sampling Theory and Applications (SampTA) , pages=
Sparse linear contextual bandits via relevance vector machines , author=. 2017 International Conference on Sampling Theory and Applications (SampTA) , pages=. 2017 , organization=
2017
-
[122]
Artificial Intelligence and Statistics , pages=
Bandit theory meets compressed sensing for high dimensional stochastic linear bandit , author=. Artificial Intelligence and Statistics , pages=. 2012 , organization=
2012
-
[123]
International Conference on Machine Learning , pages=
A simple unified framework for high dimensional bandit problems , author=. International Conference on Machine Learning , pages=. 2022 , organization=
2022
-
[124]
Proceedings of the ACM on Measurement and Analysis of Computing Systems , volume=
Dynamic regret minimization for control of non-stationary linear dynamical systems , author=. Proceedings of the ACM on Measurement and Analysis of Computing Systems , volume=
-
[125]
Conference on Learning Theory , pages=
A new algorithm for non-stationary contextual bandits: Efficient, optimal and parameter-free , author=. Conference on Learning Theory , pages=. 2019 , organization=
2019
-
[126]
the Annals of Probability , pages=
On tail probabilities for martingales , author=. the Annals of Probability , pages=. 1975 , publisher=
1975
-
[127]
Management Science, in press , year=
High-dimensional dynamic pricing under non-stationarity: Learning and earning with change-point detection , author=. Management Science, in press , year=
-
[128]
Management Science , volume=
A statistical learning approach to personalization in revenue management , author=. Management Science , volume=. 2022 , publisher=
2022
-
[129]
International Conference on Machine Learning , pages=
Pricing with Contextual Elasticity and Heteroscedastic Valuation , author=. International Conference on Machine Learning , pages=. 2024 , organization=
2024
-
[130]
Journal of the American Statistical Association , doi=
Contextual dynamic pricing: Algorithms, optimality, and local differential privacy constraints , author=. Journal of the American Statistical Association , doi=. 2026 , publisher=
2026
-
[131]
Advances in Neural Information Processing Systems , volume=
Improved algorithms for contextual dynamic pricing , author=. Advances in Neural Information Processing Systems , volume=
-
[132]
International Conference on Artificial Intelligence and Statistics , pages=
A simple approach for non-stationary linear bandits , author=. International Conference on Artificial Intelligence and Statistics , pages=. 2020 , organization=
2020
-
[133]
Non-stationary contextual pricing with safety constraints , author=
-
[134]
Conference on Learning Theory , pages=
Tracking most significant arm switches in bandits , author=. Conference on Learning Theory , pages=. 2022 , organization=
2022
-
[135]
Proceedings of the Thirty-Second Conference on Learning Theory , pages =
Adaptively Tracking the Best Bandit Arm with an Unknown Number of Distribution Changes , author =. Proceedings of the Thirty-Second Conference on Learning Theory , pages =. 2019 , editor =
2019
-
[136]
Journal of the Royal Statistical Society Series B: Statistical Methodology , volume=
Multiscale change point inference , author=. Journal of the Royal Statistical Society Series B: Statistical Methodology , volume=. 2014 , publisher=
2014
-
[137]
Journal of the royal statistical society series b: statistical methodology , volume=
Inference for multiple change points in time series via likelihood ratio scan statistics , author=. Journal of the royal statistical society series b: statistical methodology , volume=. 2016 , publisher=
2016
-
[138]
Auer, P., Gajane, P., and Ortner, R. (2019). Adaptively tracking the best bandit arm with an unknown number of distribution changes. In Beygelzimer, A. and Hsu, D., editors, Proceedings of the Thirty-Second Conference on Learning Theory , volume 99 of Proceedings of Machine Le...
2019
-
[139]
R., Farrokhnia, R
Baker, S. R., Farrokhnia, R. A., Meyer, S., Pagel, M., and Yannelis, C. (2020). How does household spending respond to an epidemic? consumption during the 2020 covid-19 pandemic. The Review of Asset Pricing Studies , 10(4):834--862
2020
-
[140]
and Keskin, N
Ban, G.-Y. and Keskin, N. B. (2021). Personalized dynamic pricing with machine learning: High-dimensional features and heterogeneous elasticity. Management Science , 67(9):5549--5568
2021
-
[141]
Bastani, H., Simchi-Levi, D., and Zhu, R. (2022). Meta dynamic pricing: Transfer learning across experiments. Management Science , 68(3):1865--1881
2022
-
[142]
Berge, C. (1957). Two theorems in graph theory. Proceedings of the National Academy of Sciences , 43(9):842--844
1957
-
[143]
Besbes, O., Gur, Y., and Zeevi, A. (2014). Stochastic multi-armed-bandit problem with non-stationary rewards. Advances in Neural Information Processing Systems , 27
2014
-
[144]
and Zeevi, A
Besbes, O. and Zeevi, A. (2009). Dynamic pricing without knowing the demand function: Risk bounds and near-optimal algorithms. Operations Research , 57(6):1407--1420
2009
-
[145]
and Zeevi, A
Besbes, O. and Zeevi, A. (2011). On the minimax complexity of pricing in a changing environment. Operations Research , 59(1):66--79
2011
-
[146]
Besson, L., Kaufmann, E., Maillard, O.-A., and Seznec, J. (2022). Efficient change-point detection for tackling piecewise-stationary bandits. Journal of Machine Learning Research
2022
-
[147]
and Rusmevichientong, P
Broder, J. and Rusmevichientong, P. (2012). Dynamic pricing under a general parametric choice model. Operations Research , 60(4):965--980
2012
-
[148]
Cao, Y., Zheng, W., Kveton, B., and Xie, Y. (2019). Nearly optimal adaptive procedure for piecewise-stationary bandit: a change-point detection approach. AISTATS, Okinawa, Japan
2019
-
[149]
Chai, J., Duan, Y., Fan, J., and Wang, K. (2024). Localized exploration in contextual dynamic pricing achieves dimension-free regret. arXiv preprint arXiv:2412.19252
2024 arXiv
-
[150]
and Gallego, G
Chen, N. and Gallego, G. (2019). Welfare analysis of dynamic pricing. Management Science , 65(1):139--151
2019
-
[151]
and Gallego, G
Chen, N. and Gallego, G. (2021). Nonparametric pricing analytics with customer covariates. Operations Research , 69(3):974--984
2021
-
[152]
Chen, X., Miao, S., and Wang, Y. (2022a). Differential privacy in personalized pricing with nonparametric demand models. Operations Research
-
[153]
Chen, X., Owen, Z., Pixton, C., and Simchi-Levi, D. (2022b). A statistical learning approach to personalization in revenue management. Management Science , 68(3):1923--1937
1923
-
[154]
Chen, Y., Lee, C.-W., Luo, H., and Wei, C.-Y. (2019). A new algorithm for non-stationary contextual bandits: Efficient, optimal and parameter-free. In Conference on Learning Theory , pages 696--726. PMLR
2019
-
[155]
Chen, Y., Wen, Z., and Xie, Y. (2023). Dynamic pricing in an evolving and unknown marketplace. Management Science, to appear
2023
-
[156]
C., Simchi-Levi, D., and Wang, H
Cheung, W. C., Simchi-Levi, D., and Wang, H. (2017). Dynamic pricing and demand learning with limited price experimentation. Operations Research , 65(6):1722--1731
2017
-
[157]
C., Simchi-Levi, D., and Zhu, R
Cheung, W. C., Simchi-Levi, D., and Zhu, R. (2019). Learning to optimize under non-stationarity. In The 22nd International Conference on Artificial Intelligence and Statistics , pages 1079--1087. PMLR
2019
-
[158]
C., Simchi-Levi, D., and Zhu, R
Cheung, W. C., Simchi-Levi, D., and Zhu, R. (2022). Hedging the drift: Learning to optimize under nonstationarity. Management Science , 68(3):1696--1713
2022
-
[159]
den Boer, A. V. and Zwart, B. (2015). Dynamic pricing and learning with finite inventories. Operations Research , 63(4):965--978
2015
-
[160]
Farias, V. F. and Van Roy, B. (2010). Dynamic pricing with a prior on market response. Operations Research , 58(1):16--29
2010
-
[161]
Frick, K., Munk, A., and Sieling, H. (2014). Multiscale change point inference. Journal of the Royal Statistical Society Series B: Statistical Methodology , 76(3):495--580
2014
-
[162]
Fryzlewicz, P. (2014). Wild binary segmentation for multiple change-point detection. The Annals of Statistics , 42(6):2243--2281
2014
-
[163]
and Moulines, E
Garivier, A. and Moulines, E. (2011). On upper-confidence bound policies for switching bandit problems. In International Conference on Algorithmic Learning Theory , pages 174--188. Springer
2011
-
[164]
M., Keskin, N
Harrison, J. M., Keskin, N. B., and Zeevi, A. (2012). Bayesian dynamic pricing policies: Learning and earning under a binary prior distribution. Management Science , 58(3):570--586
2012
-
[165]
B., Li, Y., and Song, J.-S
Keskin, N. B., Li, Y., and Song, J.-S. (2022). Data-driven dynamic pricing and ordering with perishable inventory in a changing environment. Management Science , 68(3):1938--1958
2022
-
[166]
Keskin, N. B. and Zeevi, A. (2014). Dynamic pricing with an unknown demand model: Asymptotically optimal semi-myopic policies. Operations Research , 62(5):1142--1167
2014
-
[167]
Keskin, N. B. and Zeevi, A. (2017). Chasing demand: Learning and earning in a changing environment. Mathematics of Operations Research , 42(2):277--307
2017
-
[168]
Liu, F., Lee, J., and Shroff, N. (2018). A change-detection based framework for piecewise-stationary multi-armed bandit problem. Proceedings of the AAAI Conference on Artificial Intelligence , 32(1)
2018
-
[169]
McOuat, A., Kuijpers, D., Ib 'a n ez, P., and Drassinower, R. (2024). A turning point for private brands: How retailers can seize the opportunity. McKinsey & Company. Accessed: 2026-06-08
2024
-
[170]
Nambiar, M., Simchi-Levi, D., and Wang, H. (2019). Dynamic learning and pricing with model misspecification. Management Science , 65(11):4980--5000
2019
-
[171]
and Neelamegham, R
Parker, P. and Neelamegham, R. (1997). Price elasticity dynamics over the product life cycle: A study of consumer durables. Marketing Letters , 8(2):205--216
1997
-
[172]
and Kpotufe, S
Suk, J. and Kpotufe, S. (2022). Tracking most significant arm switches in bandits. In Conference on Learning Theory , pages 2160--2182. PMLR
2022
-
[173]
Tsybakov, A. (2009). Introduction to Nonparametric Estimation . Springer, New York
2009
-
[174]
Wang, H., Talluri, K., and Li, X. (2025). On dynamic pricing with covariates. Operations Research , 73(4):1932--1943
2025
-
[175]
Wang, Y. (2023). On adaptivity in nonstationary stochastic optimization with bandit feedback. Operations Research
2023
-
[176]
Wang, Y., Chen, B., and Simchi-Levi, D. (2021). Multimodal dynamic pricing. Management Science , 67(10):6136--6152
2021
-
[177]
and Luo, H
Wei, C.-Y. and Luo, H. (2021). Non-stationary reinforcement learning without prior knowledge: An optimal black-box approach. In Conference on learning theory , pages 4300--4354. PMLR
2021
-
[178]
and Wang, Y.-X
Xu, J. and Wang, Y.-X. (2024). Pricing with contextual elasticity and heteroscedastic valuation. In International Conference on Machine Learning , pages 55286--55304. PMLR
2024
-
[179]
Yau, C. Y. and Zhao, Z. (2016). Inference for multiple change points in time series via likelihood ratio scan statistics. Journal of the royal statistical society series b: statistical methodology , 78(4):895--916
2016
-
[180]
Yu, Y. (2020). A review on minimax rates in change point detection and localisation. arXiv preprint arXiv:2011.01857
2020 arXiv
-
[181]
Zhao, Z., Jiang, F., and Yu, Y. (2026a). Contextual dynamic pricing: Algorithms, optimality, and local differential privacy constraints. Journal of the American Statistical Association , (just-accepted):1--28
-
[182]
Zhao, Z., Jiang, F., Yu, Y., and Chen, X. (2026b). High-dimensional dynamic pricing under non-stationarity: Learning and earning with change-point detection. Management Science, in press
Reviewed July 31, 2026 · model on record in the stance chip above.
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