Pith. sign in

REVIEW 3 major objections 6 minor 1 cited by

Learning an Optimal Assortment Policy under Observational Data

T0 review · 3 major / 6 minor · reviewed 2026-08-08 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Per-item coverage is both sufficient and necessary for near-optimal offline assortment learning under the MNL model; PRB achieves the minimax rate and matching lower bounds show no weaker condition exists.

desk verdict A real advance on the upper bound; the necessity lower bound is not proven as written due to a concrete gap in the Fano/KL argument. read the letter →

arxiv 2502.06777 v4 pith:5CUJG4A5 submitted 2025-02-10 stat.ML cs.LGmath.OCmath.STstat.TH

Yuxuan Han , Han Zhong , Miao Lu , Jose Blanchet , Zhengyuan Zhou This is my paper · ORCID
classification stat.MLcs.LGmath.OCmath.STstat.TH MSC 62C2090B60
keywords offlineassortmentoptimizationmultinomiallogitmodelpessimisticestimationrank-breakingoptimalitemcoverageminimaxlowerboundobservationaldatasuboptimalitygap
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks what historical data are truly needed to learn a near-optimal product assortment when customers choose according to the multinomial logit (MNL) model, the standard choice model in which each item's selection probability is proportional to its attraction value. The authors establish that it is enough for each item in the optimal assortment to appear individually in some observed assortment: seeing the whole optimal assortment together, as earlier work required, is not necessary. They prove this with an algorithm, Pessimistic Rank-Breaking (PRB), which achieves a suboptimality gap of $\widetilde{O}(K/\sqrt{\min_{i\in S^*} n_i})$ for non-uniform rewards and $\widetilde{O}(\sqrt{K/\min_{i\in S^*} n_i})$ for uniform rewards, and they prove matching lower bounds. Together these bounds show that the per-item coverage count $\min_{i\in S^*} n_i$ is the exact statistical quantity governing offline learnability, and that a $\sqrt{K}$ gap separates the uniform-reward and non-uniform-reward settings.

What carries the argument

The central object is Pessimistic Rank-Breaking (PRB), which combines a rank-breaking estimator with a pessimistic optimization step. For each item $j$, PRB counts $\tau_{j0}$, the number of records in which $j$ was offered and the customer chose either $j$ or nothing, and $\tau_j$, the number in which $j$ was chosen; it forms the empirical pairwise win rate $\hat p_j=\tau_j/\tau_{j0}$, shrinks it to a lower confidence bound $p^{\mathrm{LCB}}_j$, and maps it to a pessimistic attraction value $v^{\mathrm{LCB}}_j=p^{\mathrm{LCB}}_j/(1-p^{\mathrm{LCB}}_j)$. The assortment returned maximizes expected revenue under $\{v^{\mathrm{LCB}}_j\}$, a standard polynomial-time subproblem. Lemma 4.1 is the load-bearing monotonicity step: if estimated attractions never exceed true attractions, the revenue gap is bounded by a sum over items in the optimal assortment only, which is why only per-item coverage is needed rather than full-assortment coverage. The lower bound is carried by a packing of $K$-subsets that are $K/4$-separated, Fano's inequality, and a KL-divergence calculation showing that each informative observation contributes only $O(\epsilon^2)$; the hard instance adds zero-revenue high-attraction filler items to make informative choices rare.

What would settle it

Construct the paper's hard instance: $K$ optimal items with attraction $1/K+\epsilon$, $K$ competitive items with attraction $1/K$, and zero-revenue filler items with attraction $1$, where each optimal item appears in exactly $n_{\min}$ observed assortments and the full optimal assortment never appears. Run PRB and track the suboptimality gap as $n_{\min}$ grows: in the non-uniform setting it should follow $\Omega(K/\sqrt{n_{\min}})$ and in the uniform setting $\Omega(\sqrt{K/n_{\min}})$; observing a faster decay would contradict the lower bound, while a direct counterexample to the imported LCB bound would invalidate the upper-bound proof.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is a complete minimax characterization of offline assortment optimization under the MNL model. Any algorithm must incur a suboptimality gap of order $\Omega(K/\sqrt{\min_{i\in S^*} n_i})$ when rewards differ across items, and PRB attains this rate up to logarithmic factors; when rewards are identical, the analogous rate is $\Theta(\sqrt{K/\min_{i\in S^*} n_i})$ with a matching lower bound. The operative condition is therefore optimal item coverage: each item in the optimal assortment $S^*$ must show up in the historical data often enough, while observations of the full assortment $S^*$ itself are not required. The paper further shows the prior full-assortment coverage condition is strictly stronger in general, and that no algorithm can do better than PRB's per-item dependency.

Load-bearing premise

The proof's main load-bearing premise is that a certain probability bound on the rank-breaking estimator, taken from an online setting with fixed constants, still holds in the offline setting; if it fails, the claimed rates do not follow.

Editorial extensions

If this is right

  • Retailers can plan data collection by ensuring every item that might enter the optimal assortment appears in enough historical assortments; they do not need to have ever sold or even offered the entire optimal combination.
  • The quantity $\min_{i\in S^*} n_i$ becomes a pre-hoc diagnostic: a dataset is adequate exactly when this per-item coverage number is large enough for the target gap.
  • In the non-uniform reward setting the difficulty scales linearly in assortment size $K$, while in the uniform setting it scales as $\sqrt{K}$; this $\sqrt{K}$ gap is an offline phenomenon and does not appear in online MNL bandits.
  • PRB is computationally light: its estimator is closed-form and its final optimization reuses existing polynomial-time assortment solvers, so the method remains practical for large $N$ and $n$.
  • The matching lower bounds rule out any algorithm achieving a better suboptimality gap from the same coverage condition, so the per-item coverage requirement is not an artifact of PRB's design.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper does not prove it, but its experiments suggest pessimistic MLE-based algorithms may also be governed by $\min_{i\in S^*} n_i$ rather than by full-assortment count $n_{S^*}$; a direct guarantee for such algorithms under item coverage would be a natural next step.
  • The hard-instance construction implies that in non-uniform reward settings, the presence of zero-revenue items with high attraction values is what makes offline learning hard; this suggests data-collection protocols should avoid pairing candidate items with dominating filler products, or should weight such records appropriately.
  • The packing-plus-Fano proof structure should extend to other random-utility choice models that admit pairwise rank-breaking estimators, giving analogous per-item coverage characterizations for nested logit or exponomial demand.
  • A practical extension the authors do not address: when the optimal set $S^*$ is unknown, the coverage requirement must be enforced for every item with a chance of being optimal, so an adaptive data-collection rule based on preliminary estimates could improve sample efficiency.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper studies offline assortment optimization under the Multinomial Logit (MNL) model with a cardinality constraint K, using only pre-collected choice-assortment data. It proposes Pessimistic Rank-Breaking (PRB), which estimates pairwise choice probabilities by rank-breaking and then optimizes revenue under a pessimistic lower-confidence-bound estimate of the attraction parameters. The claimed results are near-minimax suboptimality bounds: eO(K/sqrt(min_{i in S*} n_i)) for non-uniform rewards and eO(sqrt(K/min_{i in S*} n_i)) for uniform rewards, with matching lower bounds. The authors interpret these rates as showing that optimal item coverage, rather than full optimal-assortment coverage, is sufficient and necessary for efficient offline learning. The upper-bound proof reduces the suboptimality gap to estimation errors of items in S* via a pessimism lemma (Lemma 4.1), while the lower-bound proof uses a Fano-style packing construction over optimal item sets.

Significance. If the results are correct, this is a substantial contribution: it relaxes the assortment-level coverage condition of Dong et al. (2023) to item-level coverage, gives a simple and computationally light algorithm, and provides a clean minimax characterization. The sqrt(K) gap between the uniform and non-uniform reward settings is an interesting structural insight that does not appear in the online MNL setting. The upper-bound argument is structurally sound and largely self-contained, and the lower-bound construction is adversarial but transparent. However, as written, the necessity half of the main claim is not established because the KL-divergence averaging step in the lower-bound proof is invalid; a concrete repair of the packing argument is needed before the claimed characterization is proven.

major comments (3)
  1. [Section 5.3] The displayed bound max_{(r,v),(r',v')} D(P_{r,v} || P_{r',v'}) <= C1 K / 4 does not follow from Lemma 5.4. Lemma 5.4 gives a per-item divergence bound of 5 epsilon^2 only for items in the symmetric difference Delta = Nopt(r,v) triangle Nopt(r',v'). Since D(P_{r,v} || P_{r',v'}) = n_min times the sum over these items, with epsilon^2 = C1/(20 n_min) the total is C1 |Delta| / 4, not C1 K / 4. The sets Nopt are arbitrary K-subsets of [4K], so |Delta| can be as large as 2K, and the packing condition Delta >= K/4 in Lemma 5.1 imposes no upper bound. The average KL term in Fano's inequality can therefore be as large as C1 K / 2, making the final lower bound non-positive. The proof needs a packing with all pairwise Delta <= K, or an alternative averaging argument, before Theorem 4.3 follows.
  2. [Section 5.2] The application of Fano's lemma has a separation-parameter error. Lemma 5.1 guarantees Delta(S,S') >= K/4 for all pairs, so in Lemma 5.3 the 2 delta-separation parameter gives delta = K/8, not delta0 = K/4 as stated in the text. Moreover, the displayed inequality after Lemma 5.3 has a factor K outside the parentheses, whereas Lemma 5.3 yields a factor delta. These constant errors are repairable without changing the rate, but the derivation as written is not a valid instance of Fano's lemma.
  3. [Appendix A.4, Proposition A.3] Theorem A.1, and hence Theorems 4.2 and 4.4, rest entirely on Proposition A.3, which is imported from Saha and Gaillard (2024) without proof and without verifying that the estimator in Algorithm 1 satisfies the exact hypotheses of that proposition. A direct substitution of Proposition A.3 together with the paper's lower bound tau_i0 >= (1+v_i) T_i / 2 gives a first error term of order 8 sqrt(v_i(1+v_i) log(N/delta) / T_i), not sqrt(4 v_i(1+v_i) log(N/delta) / T_i) as claimed in Theorem A.1. The authors should prove the required concentration and one-sided-correctness statement for PRB in this paper, or give a precise theorem reference and verify that the constants match.
minor comments (6)
  1. [Algorithm 1] The algorithm does not specify what to do when tau_j0 = 0, although the formula for pLCB_j divides by tau_j0; a convention such as setting vLCB_j = 0 in that case should be stated.
  2. [Section A.2] The proof heading 'Proof of Theorem 4.5' should be 'Proof of Theorem 4.4', since the theorem proved there is the uniform-reward upper bound.
  3. [Lemma 5.1 proof] The proof refers to a 'maximal K/2-packing' while the covering argument uses K/4-neighborhoods; the packing parameter should be K/4, or the terminology should be corrected and made consistent.
  4. [Section 1 and Table 1] In the introduction, the non-uniform upper bound is printed as eO(K sqrt(max_{i in S*} n_i)), which contradicts the correct expression eO(K / sqrt(min_{i in S*} n_i)) given in Table 1 and Theorem 4.2; this appears to be a typo that should be fixed.
  5. [Figure 1] The caption uses epsilon = 0.1/sqrt(K) and epsilon = 1/sqrt(nK), while the experimental setup text says epsilon = 0.05 and epsilon = 1/(10 sqrt(nK)); the notation should be unified.
  6. [Lemma A.2 proof] The proof asserts without argument that optimality of S_v under v implies R(S_v; v) <= r_j for every j in S_v; this is true (compare R(S_v;v) with R(S_v \ {j};v)), but the standard one-line justification should be included.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the upper and lower bounds are derived from independent statistical tools (Fano, Freedman, rank-breaking bounds) rather than from the conclusions they claim to establish.

full rationale

The derivation chain is self-contained in the relevant sense. The upper bounds (Theorems 4.2 and 4.4) follow from Lemma 4.1, a pessimistic-revenue decomposition proved in Appendix A.3, together with Proposition A.3, a finite-sample lower-confidence-bound result imported from Saha and Gaillard (2024). That citation is external, has no author overlap with this paper, and is not used to define the target result; the fact that Proposition A.3 is not re-proved for this exact algorithm is a verification or correctness concern, not circularity. The lower bounds (Theorems 4.3 and 4.5) use a standard Fano reduction: Lemma 5.1 constructs a packing, Lemma 5.2 converts suboptimality into set distance, and Lemma 5.4 bounds pairwise KL divergences. No fitted constant is renamed as a prediction; the hard-instance parameters are adversarial but are not derived from the algorithm's output. The central claim, that the relevant complexity measure is the minimum item coverage among optimal-assortment items, is supported by matching upper and lower bounds over constructed instances rather than by defining the quantity to match. A caveat unrelated to circularity: the Fano step in Section 5.3 appears to contain a proof gap, since the stated bound max_{pairs} D(P_{r,v} || P_{r',v'}) <= C1 K/4 seems to require |Delta| <= K while Lemma 5.1 only enforces Delta >= K/4, and Proposition A.3 is imported without proof. These are correctness risks, not instances where a result reduces to its own input. Because no such reduction is present, the circularity score is 0.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The central claims rest on the MNL model, the conditional independence assumption, the item-coverage condition, and imported concentration bounds. The only constants chosen by hand are the lower-bound construction parameters epsilon and epsilon', which are adversarial choices rather than fitted data parameters; these contain the factor-of-two error that breaks the Fano argument.

free parameters (2)
  • epsilon (non-uniform lower bound) = sqrt(C1/(20 n_min)) as stated in the paper; should be sqrt(C1/(40 n_min)) to make Fano work
    Adversarial choice in the hard instance construction. With the stated value the KL bound is twice the claimed value and the Fano lower bound vanishes.
  • epsilon' (uniform lower bound) = sqrt(C1/(20 K n_min))
    Same factor-of-two issue as epsilon. The stated value undercounts the symmetric difference of the two optimal sets by a factor of 2.
assumptions (7)
  • domain assumption MNL choice model with attraction parameters v and revenue vector r
    The entire problem is defined by this model in Section 3.
  • domain assumption Conditional independence of choices given assortments
    Assumed in Section 3 for the offline dataset; needed for the concentration inequalities used in the upper bound.
  • domain assumption Item coverage condition n_i >= 256(1+KV) log(N/delta) for all i in S*
    Assumption in Theorems 4.2 and 4.4; the paper's goal is to show this is the minimal such condition.
  • standard math Fano's inequality
    Used in Lemma 5.3 for the lower-bound proof.
  • standard math Freedman's inequality
    Used in Appendix A.4 for the concentration of the rank-breaking estimator.
  • standard math Optimal MNL assortment satisfies r_i >= R(S*) for all i in S*
    Implicitly used in Lemma A.2's proof; a known property of MNL revenue maximization but not stated in the paper.
  • ad hoc to paper Proposition A.3 from Saha and Gaillard (2024) applies to PRB with the stated constants
    The error bound for the LCB estimator is imported from an online learning paper and not proved here; PRB differs from the algorithm analyzed in that reference.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Learning an Optimal Assortment Policy under Observational Data." pith.science (2026). https://pith.science/paper/5CUJG4A5

@misc{pith2026250206777,
  author       = {Pith},
  title        = {Pith review of: Learning an Optimal Assortment Policy under Observational Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5CUJG4A5}},
  note         = {Machine review of arXiv:2502.06777}
}
read the original abstract

We study the fundamental problem of offline assortment optimization under the Multinomial Logit (MNL) model, where sellers must determine the optimal subset of the products to offer based solely on historical customer choice data. While most existing approaches to learning-based assortment optimization focus on the online learning of the optimal assortment through repeated interactions with customers, such exploration can be costly or even impractical in many real-world settings. In this paper, we consider the offline learning paradigm and investigate the minimal data requirements for efficient offline assortment optimization. To this end, we introduce Pessimistic Rank-Breaking (PRB), an algorithm that combines rank-breaking with pessimistic estimation. We prove that PRB is nearly minimax optimal by establishing the tight suboptimality upper bound and a nearly matching lower bound. This further shows that "optimal item coverage" - where each item in the optimal assortment appears sufficiently often in the historical data - is both sufficient and necessary for efficient offline learning. This significantly relaxes the previous requirement of observing the complete optimal assortment in the data. Our results provide fundamental insights into the data requirements for offline assortment optimization under the MNL model.

Figures

Figures reproduced from arXiv: 2502.06777 by the authors.

Figure 1
Figure 1. Comparison of PRB, PASTA, and MLE in different [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Sub-optimality gap of PRB under different [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Diffusion-Based Data-Driven Assortment Optimization

    cs.LG 2026-08 conditional novelty 5.0 of 10

    A reward-guided discrete diffusion model generates near-optimal product assortments from offline choice data without assuming a parametric choice model.

Reference graph

Works this paper leans on

53 extracted references · 43 canonical work pages · cited by 1 Pith paper

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address author booktitle chapter edition editor howpublished institution journal key month note number organization pages publisher school series title type url volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 'mid.sentence := ...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

  3. [3]

    , Avadhanula, V

    Agrawal, S. , Avadhanula, V. , Goyal, V. and Zeevi, A. (2017). Thompson sampling for the mnl-bandit. In Conference on learning theory. PMLR

    work page 2017

  4. [4]

    , Avadhanula, V

    Agrawal, S. , Avadhanula, V. , Goyal, V. and Zeevi, A. (2019). Mnl-bandit: A dynamic learning approach to assortment selection. Operations Research 67 1453--1485

    work page 2019

  5. [5]

    and Semple, J

    Alptekino g lu, A. and Semple, J. H. (2016). The exponomial choice model: A new alternative for assortment and price optimization. Operations Research 64 79--93

    work page 2016

  6. [6]

    , Newman, D

    Asuncion, A. , Newman, D. et al. (2007). Uci machine learning repository

    work page 2007

  7. [7]

    , Bhandari, J

    Avadhanula, V. , Bhandari, J. , Goyal, V. and Zeevi, A. (2016). On the tightness of an lp relaxation for rational optimization and its applications. Operations Research Letters 44 612--617

    work page 2016

  8. [8]

    , Goyal, V

    Aznag, A. , Goyal, V. and Perivier, N. (2021). Mnl-bandit with knapsacks. arXiv preprint arXiv:2106.01135

    arXiv 2021

Show all 53 references
  1. [9]

    , Garassino, A

    Berbeglia, G. , Garassino, A. and Vulcano, G. (2022). A comparative empirical study of discrete choice models in retail operations. Management Science 68 4005--4023

    2022

  2. [10]

    , Gallego, G

    Blanchet, J. , Gallego, G. and Goyal, V. (2016). A markov chain approximation to choice modeling. Operations Research 64 886--905

    2016

  3. [11]

    Blanchet, J. , Lu, M. , Zhang, T. and Zhong, H. (2023). Double pessimism is provably efficient for distributionally robust offline reinforcement learning: Generic algorithm and robust partial coverage. Advances in Neural Information Processing Systems 36

    2023

  4. [12]

    and Gallien, J

    Caro, F. and Gallien, J. (2007). Dynamic assortment with demand learning for seasonal consumer goods. Management science 53 276--292

    2007

  5. [13]

    , Liu, M

    Chen, X. , Liu, M. , Wang, Y. and Zhou, Y. (2024). A re-solving heuristic for dynamic assortment optimization with knapsack constraints. arXiv preprint arXiv:2407.05564

    2024

  6. [14]

    , Shi, C

    Chen, X. , Shi, C. , Wang, Y. and Zhou, Y. (2021 a ). Dynamic assortment planning under nested logit models. Production and Operations Management 30 85--102

    2021

  7. [15]

    and Wang, Y

    Chen, X. and Wang, Y. (2018). A note on a tight lower bound for capacitated mnl-bandit assortment selection models. Operations Research Letters 46 534--537

    2018

  8. [16]

    , Wang, Y

    Chen, X. , Wang, Y. and Zhou, Y. (2021 b ). Optimal policy for dynamic assortment planning under multinomial logit models. Mathematics of Operations Research 46 1639--1657

    2021

  9. [17]

    Cheung, W. C. and Simchi-Levi, D. (2017). Assortment optimization under unknown multinomial logit choice models. arXiv preprint arXiv:1704.00108

    2017 arXiv

  10. [18]

    Daganzo, C. (2014). Multinomial probit: the theory and its application to demand forecasting. Elsevier

    2014

  11. [19]

    , Gallego, G

    Davis, J. , Gallego, G. and Topaloglu, H. (2013). Assortment planning under the multinomial logit model with totally unimodular constraint structures. Work in Progress

    2013

  12. [20]

    Davis, J. M. , Gallego, G. and Topaloglu, H. (2014). Assortment optimization under variants of the nested logit model. Operations Research 62 250--273

    2014

  13. [21]

    Dong, J. , Mo, W. , Qi, Z. , Shi, C. , Fang, E. X. and Tarokh, V. (2023). Pasta: pessimistic assortment optimization. In International Conference on Machine Learning. PMLR

    2023

  14. [22]

    , Yang, Z

    Jin, Y. , Yang, Z. and Wang, Z. (2021). Is pessimism provably efficient for offline rl? In International Conference on Machine Learning. PMLR

    2021

  15. [23]

    , Zhou, A

    Kumar, A. , Zhou, A. , Tucker, G. and Levine, S. (2020). Conservative q-learning for offline reinforcement learning. Advances in Neural Information Processing Systems 33 1179--1191

    2020

  16. [24]

    Le Cam, L. (2012). Asymptotic methods in statistical decision theory. Springer Science & Business Media

    2012

  17. [25]

    and Oh, M.-h

    Lee, J. and Oh, M.-h. (2024). Nearly minimax optimal regret for multinomial logistic bandit. arXiv preprint arXiv:2405.09831

    2024

  18. [26]

    , Luo, Q

    Li, S. , Luo, Q. , Huang, Z. and Shi, C. (2022). Online learning for constrained assortment optimization under markov chain choice model. Available at SSRN 4079753

    2022

  19. [27]

    Liu, Z. , Lu, M. , Wang, Z. , Jordan, M. and Yang, Z. (2022). Welfare maximization in competitive equilibrium: Reinforcement learning for markov exchange economy. In International Conference on Machine Learning. PMLR

    2022

  20. [28]

    , Min, Y

    Lu, M. , Min, Y. , Wang, Z. and Yang, Z. (2023). Pessimism in the face of confounders: Provably efficient offline reinforcement learning in partially observable markov decision processes. In The Eleventh International Conference on Learning Representations

    2023

  21. [29]

    Luce, R. D. (1959). Individual choice behavior, vol. 4. Wiley New York

    1959

  22. [30]

    McFadden, D. (1977). Modelling the choice of residential location

    1977

  23. [31]

    and Train, K

    McFadden, D. and Train, K. (2000). Mixed mnl models for discrete response. Journal of applied Econometrics 15 447--470

    2000

  24. [32]

    and Iyengar, G

    Oh, M.-h. and Iyengar, G. (2021). Multinomial logit contextual bandits: Provable optimality and practicality. In Proceedings of the AAAI conference on artificial intelligence, vol. 35

    2021

  25. [33]

    Ou, M. , Li, N. , Zhu, S. and Jin, R. (2018). Multinomial logit bandit with linear utility functions. arXiv preprint arXiv:1805.02971

    2018 arXiv

  26. [34]

    and Goyal, V

    Perivier, N. and Goyal, V. (2022). Dynamic pricing and assortment under a contextual mnl demand. Advances in Neural Information Processing Systems 35 3461--3474

    2022

  27. [35]

    , Shamir, O

    Rakhlin, A. , Shamir, O. and Sridharan, K. (2012). Making gradient descent optimal for strongly convex stochastic optimization. In Proceedings of the 29th International Coference on International Conference on Machine Learning

    2012

  28. [36]

    , Zhu, B

    Rashidinejad, P. , Zhu, B. , Ma, C. , Jiao, J. and Russell, S. (2021). Bridging offline reinforcement learning and imitation learning: A tale of pessimism. Advances in Neural Information Processing Systems 34 11702--11716

    2021

  29. [37]

    , Zhu, H

    Rashidinejad, P. , Zhu, H. , Yang, K. , Russell, S. and Jiao, J. (2023). Optimal conservative offline RL with general function approximation via augmented lagrangian. In The Eleventh International Conference on Learning Representations

    2023

  30. [38]

    , Shen, Z.-J

    Rusmevichientong, P. , Shen, Z.-J. M. and Shmoys, D. B. (2010). Dynamic assortment optimization with a multinomial logit choice model and capacity constraint. Operations research 58 1666--1680

    2010

  31. [39]

    and Gaillard, P

    Saha, A. and Gaillard, P. (2024). Stop relying on no-choice and do not repeat the moves: Optimal, efficient and practical algorithms for assortment optimization. arXiv preprint arXiv:2402.18917

    2024 arXiv

  32. [40]

    and Gopalan, A

    Saha, A. and Gopalan, A. (2019). Active ranking with subset-wise preferences. In The 22nd International Conference on Artificial Intelligence and Statistics. PMLR

    2019

  33. [41]

    and Zeevi, A

    Saur \'e , D. and Zeevi, A. (2013). Optimal dynamic assortment planning with demand learning. Manufacturing & Service Operations Management 15 387--404

    2013

  34. [42]

    Shi, L. , Li, G. , Wei, Y. , Chen, Y. and Chi, Y. (2022). Pessimistic q-learning for offline reinforcement learning: Towards optimal sample complexity. In International conference on machine learning. PMLR

    2022

  35. [43]

    and Van Ryzin, G

    Talluri, K. and Van Ryzin, G. (2004). Revenue management under a general discrete choice model of consumer behavior. Management Science 50 15--33

    2004

  36. [44]

    Train, K. E. (2009). Discrete choice methods with simulation. Cambridge university press

    2009

  37. [45]

    Tsybakov, A. B. (2008). Introduction to Nonparametric Estimation. 1st ed. Springer Publishing Company, Incorporated

    2008

  38. [46]

    and Sun, W

    Uehara, M. and Sun, W. (2021). Pessimistic model-based offline reinforcement learning under partial coverage. In International Conference on Learning Representations

    2021

  39. [47]

    , Cheng, C.-A

    Xie, T. , Cheng, C.-A. , Jiang, N. , Mineiro, P. and Agarwal, A. (2021). Bellman-consistent pessimism for offline reinforcement learning. Advances in neural information processing systems 34 6683--6694

    2021

  40. [48]

    , Zhong, H

    Xiong, W. , Zhong, H. , Shi, C. , Shen, C. , Wang, L. and Zhang, T. (2023). Nearly minimax optimal offline reinforcement learning with linear function approximation: Single-agent mdp and markov game. In International Conference on Learning Representations (ICLR)

    2023

  41. [49]

    Yu, B. (1997). Assouad, fano, and le cam. In Festschrift for Lucien Le Cam: research papers in probability and statistics. Springer, 423--435

    1997

  42. [50]

    , Thomas, G

    Yu, T. , Thomas, G. , Yu, L. , Ermon, S. , Zou, J. Y. , Levine, S. , Finn, C. and Ma, T. (2020). Mopo: Model-based offline policy optimization. Advances in Neural Information Processing Systems 33 14129--14142

    2020

  43. [51]

    , Huang, B

    Zhan, W. , Huang, B. , Huang, A. , Jiang, N. and Lee, J. (2022). Offline reinforcement learning with realizability and single-policy concentrability. In Conference on Learning Theory. PMLR

    2022

  44. [52]

    and Sugiyama, M

    Zhang, Y.-J. and Sugiyama, M. (2024). Online (multinomial) logistic bandit: Improved regret and constant computation cost. Advances in Neural Information Processing Systems 36

    2024

  45. [53]

    , Xiong, W

    Zhong, H. , Xiong, W. , Tan, J. , Wang, L. , Zhang, T. , Wang, Z. and Yang, Z. (2022). Pessimistic minimax value iteration: Provably efficient equilibrium learning from offline datasets. In International Conference on Machine Learning. PMLR

    2022

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.