Pith. sign in

REVIEW 3 major objections 4 minor 81 references

Minimax and Bayes Optimal Best-Arm Identification

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read A single two-stage strategy is exactly minimax and Bayes optimal for best-arm identification.

desk verdict A serious, likely-correct lower-bound theory and a novel analysis of the sharp constants, but the matching upper bounds for K >= 3 rest on an unproven numerical saddle-point oracle, so the paper's headline claim is conditional. read the letter →

arxiv 2506.24007 v6 pith:NXQS7K6M submitted 2025-06-30 econ.EM cs.LGmath.STstat.MEstat.MLstat.TH

Masahiro Kato This is my paper
classification econ.EMcs.LGmath.STstat.MEstat.MLstat.TH MSC 62L0562C2062F1262F15
keywords best-armidentificationfixed-budgetsimpleregretminimaxoptimalityBayesGaussiangameNeymanallocationlocalasymptoticnormality
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 claims to settle a core question in fixed-budget best-arm identification: how to allocate a fixed sample budget across $K$ treatments so that the expected welfare loss from recommending a suboptimal treatment is as small as possible. It proposes a single strategy, TS-SPAS, that first samples all arms equally to estimate variances and discard clearly inferior arms, then allocates the remaining samples according to the saddle point of a Gaussian minimax game and recommends an arm using the decision rule from the same game. The paper proves that this rule is asymptotically minimax optimal, with worst-case simple regret of order $C_{\mathrm{mm}}/\sqrt{T}$, and asymptotically Bayes optimal, with prior-averaged simple regret of order $C_{\mathrm{Bayes}}/T$, and that the upper bounds match lower bounds exactly, constants included. A sympathetic reader would see the contribution as showing that worst-case and prior-average optimality are not in tension: one distribution-free procedure achieves both without knowing the outcome distributions or the prior.

What carries the argument

The load-bearing object is the Gaussian minimax game. In the proxy experiment Nature chooses a mean vector $h$, the statistician observes $X=h+Z$ with $Z\sim N(0,\mathrm{diag}(\sigma_a^2/w_a))$ for an allocation $w$ on a subset $S$ of arms, and the loss is the gap $\max_a h_a-h_A$. Its value $C_S(\sigma)=\inf_w\inf_g\sup_h E[\max_a h_a-h_A]$ yields both the sharp minimax constant (with $S=[K]$) and the Stage 2 objects: a sampling ratio $w^*$ and a decision rule $g^*$. TS-SPAS uses Stage 1 uniform sampling to estimate variances and screen to a candidate set, then in Stage 2 samples according to an approximate saddle point and recommends via the saddle-point rule. The proofs show via local asymptotic normality that the worst-case and prior-average problems reduce to this Gaussian proxy once nonlocal arms have been eliminated by large-deviation screening, and the binary special case reduces to Neyman allocation with the empirical-best rule.

What would settle it

Run TS-SPAS on a three-arm Gaussian problem with equal variances and a near-tie mean vector, using a high-accuracy numerical solver for the Gaussian minimax game; if the observed $\sqrt{T}$-scaled worst-case regret does not converge to $C_{[K]}(\sigma)$ as $T$ grows, the matching upper bound fails. Alternatively, exhibit a single instance on which the Algorithm 2 mirror-ascent routine fails to converge to an $\varepsilon_T$-minimax rule for $\varepsilon_T=o(1)$; that would refute the claim that the strategy is implementable as stated.

Watch

Extended reading notes

Core claim

The central claim is that a single two-stage adaptive experiment attains exact asymptotic optimality under both minimax and Bayes criteria for the simple regret. For minimax regret, the paper proves $\limsup_{T\to\infty}\sqrt{T}\sup_{\mu\in M^K}\mathrm{Regret}^{\delta_{\mathrm{TS-SPAS}}}_T(\mu)\le C_{\mathrm{mm}}\le \inf_{\delta}\liminf_{T\to\infty}\sqrt{T}\sup_{\mu\in M^K}\mathrm{Regret}^{\delta}_T(\mu)$, where $C_{\mathrm{mm}}$ is the value of a Gaussian minimax game over the worst-case mean vector at each variance profile. For Bayes regret, under a regular prior on the mean vector, it proves $\limsup_{T\to\infty}T\int \mathrm{Regret}^{\delta_{\mathrm{TS-SPAS}}}_T(\mu)\,dH(\mu)\le C_{\mathrm{Bayes}}\le \inf_{\delta}\liminf_{T\to\infty}T\int \mathrm{Regret}^{\delta}_T(\mu)\,dH(\mu)$, with $C_{\mathrm{Bayes}}$ an explicit sum over arm pairs of variance-weighted densities at the pairwise tie surface. The lower bounds hold against every adaptive experiment and for every fixed number of arms, and the upper bounds are attained without knowledge of the outcome distributions or the prior.

Load-bearing premise

For the upper bounds to be realized by a concrete algorithm, the second sampling stage must be able to compute an approximate saddle point of the Gaussian minimax game with error $\varepsilon_T=o(1)$ in finite time; the paper supplies only a heuristic numerical routine, with no convergence proof, runtime bound, or guarantee that the computed rule is $\varepsilon_T$-minimax.

Editorial extensions

If this is right

  • No adaptive experiment can improve on the $\sqrt{T}$ worst-case simple regret by even a constant factor: the minimax lower bound $C_{\mathrm{mm}}$ applies to every strategy in the class $A$.
  • Under a regular prior, the best possible prior-averaged regret is $C_{\mathrm{Bayes}}/T$, and TS-SPAS achieves it, so the design is unimprovable in the Bayes sense as well.
  • When only two arms survive screening, the strategy simplifies to Neyman allocation with the empirical-best recommendation and the closed-form constant $(\sigma_a+\sigma_b)c_{\mathrm{mm}}$ with $c_{\mathrm{mm}}\approx 0.1699712$.
  • The strategy does not need to know variances or the prior: Stage 1 estimates variances, and the same Gaussian game is solved with the estimated variances.
  • For Bernoulli outcomes, variance estimation can be omitted and uniform allocation suffices, because near-tie variances coincide as the mean gap shrinks.

Reading between the lines

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

  • One consequence the paper leaves implicit is that the matching constants are only as constructive as the Stage 2 saddle-point solver; a polynomial-time algorithm with an explicit $\varepsilon_T=o(1)$ guarantee would turn the upper-bound theorem into a fully implementable procedure.
  • For realistic sample sizes, the asymptotic split $T_0=T^{1-\epsilon}$ and the screening threshold are free tuning choices whose finite-sample effects are not quantified; these are natural targets for a testable extension.
  • The same Gaussian proxy game is likely to be the exact local benchmark for other adaptive-design problems with near-tie local experiments, such as fixed-confidence best-arm identification or treatment-choice experiments with covariates.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper studies fixed-budget best-arm identification under the simple-regret criterion and proposes a single two-stage strategy, TS-SPAS, that it claims is simultaneously asymptotically minimax and Bayes optimal with exact leading constants. The strategy uses a uniform pilot phase to screen obviously suboptimal arms and estimate variances, then solves a Gaussian minimax game to obtain a sampling allocation and a recommendation rule for the second stage. The main results are matching minimax lower and upper bounds (Theorems 5.1 and 5.2) and matching Bayes lower and upper bounds (Theorems 6.1 and 6.2), with the constants given by the value of a Gaussian proxy game in the minimax case and by a pairwise tie-surface integral in the Bayes case. The lower-bound proofs use local asymptotic normality and Le Cam's third lemma; the upper-bound proofs reduce local alternatives to the Gaussian proxy experiment after a screening step.

Significance. If the main claims are correct, this would be a substantial advance: it would show that one adaptive, distribution-free two-stage rule attains the sharp constant in both the worst-case and prior-average senses for fixed-budget BAI with any fixed number of arms. The use of LAN and Le Cam arguments for bandit lower bounds, combined with large-deviation screening, is a conceptually interesting and technically demanding framework. The paper also verifies that in the Bernoulli case the Bayes constant coincides with the constant conjectured/derived by Komiyama et al. (2023). However, the upper-bound theorems are conditional on the existence of a finite-time approximate saddle-point solver for the Gaussian minimax game, and the paper does not provide such a solver with a convergence guarantee. Until that gap is repaired, the central claim that a concrete, implementable strategy attains the exact constants is not fully established.

major comments (3)
  1. [Section 7.5, Appendix B, Algorithm 2, and Appendix G Step 7] The upper bounds in Theorems 5.2 and 6.2 depend on Stage 2 computing an epsilon_T-minimax saddle point (w_hat, g_hat) of the Gaussian minimax game with epsilon_T = o(1). No such computation is proven to exist in finite time. Algorithm 2 fixes a support library H arbitrarily, uses Monte Carlo estimates with no bias or variance control, and updates p by mirror ascent while treating r_ell as fixed even though r_ell depends on p through the Bayes rule g_p. Lemma 7.5 guarantees only the existence of a finite-support prior for a fixed (w, sigma, epsilon), not a uniform approximation over the outer w-search with a prescribed grid. Consequently, the premise used in Step 7 of Appendix G ('bg is computed as an epsilon_T-minimax rule') is unverified, and the claimed exact matching constants in Corollaries 5.3 and 6.3 are not certified for a concrete algorithm. This issue is load-bearing and must be fixed either by giving a provable finite-time solver or by explicitly reformulating the theorems as conditional on an oracle and moving the concrete-algorithm claim to a conjecture.
  2. [Lemma 7.2(ii) and Appendix J.1] Lemma 7.2(ii) asserts that a minimizer w* of w -> V_S(w, sigma) lies in the open simplex W_S^o and that a minimax rule exists, but the proof in Appendix J.1 is incomplete. Step 2 invokes lower semicontinuity of w -> V_S(w, sigma) without proving it, and Step 5 proves continuity only on sets already bounded away from the boundary, so it cannot establish lower semicontinuity at the boundary. The argument also does not supply the uniform version over compact M that is needed in Step 2 of Appendix G, where the proof requires an eta > 0 such that min_a w*_a(sigma(mu)) >= eta for all mu in M. Please provide a complete proof of interiority and of the uniform positive lower bound on the minimizer, or state these as explicit assumptions.
  3. [Appendix G, Step 3] The reduction from the local regime to O(1/sqrt T) near-ties is not fully justified as written. Step 2 only treats gaps with Delta(mu) >= T^{-1/4}, but Step 3 asserts that if sqrt T Regret does not tend to zero then the gap must be O(1/sqrt T) along a subsequence, 'otherwise Step 2 would force the regret to vanish.' For gaps between T^{-1/2} and T^{-1/4}, the stated Step 2 does not apply, although a similar argument with a threshold g_T satisfying g_T / T^{-1/2} -> infinity would work. Please restate the dichotomy with an appropriate threshold so that the intermediate-gap case is covered.
minor comments (4)
  1. [Section 1.1] There is a typo in the notation: 'Let PPµ denote the probability law' should read 'Let Pµ denote the probability law.'
  2. [Algorithm 1, line 30] The input cX_T is defined as sqrt(T)(bµ_{a,T})_{a in bS_T0}, but the recommendation rule bg is translation-invariant; the pseudocode should state explicitly which centered version of cX_T is used, since the proof relies on translation equivariance.
  3. [Section 8.2] The claim that in the Bayes case one may replace the saddle-point allocation by uniform allocation and still achieve C_Bayes is not proved anywhere; please supply a proof or clearly label this as a heuristic.
  4. [Lemma D.2] Lemma D.2 is stated conditional on the event {bS_T0 = [K]}, but in the proof of Theorem 5.2 it is applied after screening may have removed arms from the candidate set. Since the true best arm is retained under R_T0, the same argument works with bS_T0 replacing [K], but this should be stated explicitly to avoid a logical gap.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation chain: the matching upper and lower bounds converge to an independently defined Gaussian benchmark, and no fitted parameter is renamed as a prediction.

full rationale

The paper's sharp constants are not circular by construction. The minimax constant C_mm is defined as the value of a Gaussian proxy game (Definition 4.1 and Eq. (4)). The lower bound (Theorem 5.1, Appendix F) proves that every adaptive experiment has a local asymptotic limit at least this game value, using LAN and Le Cam's third lemma; it does not presuppose TS-SPAS. The upper bound (Theorem 5.2, Appendix G) proves that TS-SPAS, after screening and variance estimation, reduces to the same Gaussian experiment and attains the game value; the proof does not invoke the lower bound as an input. Similarly, C_Bayes is computed independently from pairwise Gaussian testing (Appendix H) and attained in the |S|=2 regime (Appendix I), where the Neyman allocation is derived rather than fitted. The equality with Komiyama et al. (2023) in the Bernoulli case (Proposition 8.1) is an identification result proved from Eq. (5), and the matching lower bound independently verifies the conjectured constant, so the overlapping-author citation is not load-bearing. The main caveat is a correctness gap, not circularity: for |S|>=3, Stage 2 relies on Algorithm 2, which has no convergence proof or finite-time epsilon_T-minimax guarantee (Section 7.5, Appendix B). If that numerical oracle fails, the upper bounds are conditional on an unverified premise; but this is missing support, not a reduction of the claimed prediction to its own inputs.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central claim uses no fitted constants. The free-parameter list is empty because the screening tuning parameters such as T0 and C_scr are asymptotic design choices, not fitted to data. The Gaussian minimax game is a mathematical construct, not an invented physical entity. The assumptions listed above are the model class and solver assumptions on which the proof depends.

assumptions (5)
  • domain assumption Outcomes belong to a mean-parameterized canonical exponential family with uniform sub-Gaussian condition and variance bounded away from 0 and infinity (Definition 3.1 and Section 3.2).
    The optimality results are stated over this model class; the proofs use finite third moments, local asymptotic normality, and sub-Gaussian concentration, all of which depend on these conditions.
  • domain assumption The parameter space M is a compact interval and the variance functions sigma_a^2 are continuous on M.
    Compactness is used for uniform convergence of variance estimators, uniform positivity of allocation weights, and dominated convergence in the Bayes argument.
  • domain assumption The prior H satisfies Assumption 6.1: uniformly bounded and uniformly continuous conditional densities.
    The Bayes lower and upper bound proofs require the prior density to be locally uniform near pairwise tie surfaces; without this condition the sharp Bayes constant may differ.
  • ad hoc to paper An o(1)-accurate approximate saddle point of the Gaussian minimax game is computable in Stage 2.
    Algorithm 2 is a heuristic Monte Carlo routine; the theorems assume such a solver exists, but no convergence proof or runtime guarantee is supplied.
  • standard math Standard minimax theorems and Hunt-Stein type invariance results for Gaussian experiments hold.
    Lemmas 7.2 and 7.6 rely on these results to guarantee existence of saddle points and translation-equivariant minimax rules.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Minimax and Bayes Optimal Best-Arm Identification." pith.science (2026). https://pith.science/paper/NXQS7K6M

@misc{pith2026250624007,
  author       = {Pith},
  title        = {Pith review of: Minimax and Bayes Optimal Best-Arm Identification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NXQS7K6M}},
  note         = {Machine review of arXiv:2506.24007}
}
read the original abstract

This study investigates minimax and Bayes optimal strategies for fixed-budget best-arm identification. We consider an adaptive procedure consisting of a sampling phase followed by a recommendation phase. Within this framework, we design an adaptive experiment to efficiently identify the best arm, defined as the one with the highest expected outcome. In our proposed strategy, the sampling phase consists of two stages. The first stage is a pilot phase, in which we allocate samples uniformly across arms to eliminate clearly suboptimal arms and to estimate outcome variances. Before entering the second stage, we solve a Gaussian minimax game, which yields a sampling policy and a decision rule. In the second stage, samples are allocated according to this policy. After the sampling phase, the procedure enters the recommendation phase, where we select an arm using the decision rule. We prove that this single strategy is simultaneously asymptotically minimax and Bayes optimal for the simple regret, and we establish upper bounds that coincide exactly with our lower bounds, including the constant terms. The lower bounds hold against every adaptive experiment and for every fixed number of arms, and the strategy attains them without knowing the outcome distributions or the prior.

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

81 extracted references · 63 canonical work pages

  1. [1]

    Neyman allocation is minimax optimal for best arm identification with two arms

    Karun Adusumilli. Neyman allocation is minimax optimal for best arm identification with two arms, 2022. a rXiv:2204.05527

    work page Pith review arXiv 2022

  2. [2]

    Risk and optimal policies in bandit experiments

    Karun Adusumilli. Risk and optimal policies in bandit experiments, 2023. a rXiv: 2112.06363

    work page Pith review arXiv 2023

  3. [3]

    How to sample and when to stop sampling: The generalized Wald problem and minimax policies

    Karun Adusumilli. How to sample and when to stop sampling: The generalized wald problem and minimax policies, 2025. a Xiv: 2210.15841

    work page Pith review arXiv 2025

  4. [4]

    Dynamically optimal treatment allocation, 2024

    Karun Adusumilli, Friedrich Geiecke, and Claudio Schilter. Dynamically optimal treatment allocation, 2024

    2024

  5. [5]

    Advanced Econometrics

    Takeshi Amemiya. Advanced Econometrics. Harvard University Press, 1985

    work page 1985

  6. [6]

    Policy choice and best arm identification: Asymptotic analysis of exploration sampling, 2021

    Kaito Ariu, Masahiro Kato, Junpei Komiyama, Kenichiro McAlinn, and Chao Qin. Policy choice and best arm identification: Asymptotic analysis of exploration sampling, 2021. a rXiv:2109.08229

    arXiv 2021

  7. [7]

    Armstrong

    Timothy B. Armstrong. Asymptotic efficiency bounds for a class of experimental designs, 2022. a rXiv:2205.02726

    arXiv 2022

  8. [8]

    Policy learning with observational data

    Susan Athey and Stefan Wager. Policy learning with observational data. Econometrica, 89 0 (1): 0 133--161, 2021

    work page 2021

Show all 81 references
  1. [9]

    Bayesian fixed-budget best-arm identification, 2023

    Alexia Atsidakou, Sumeet Katariya, Sujay Sanghavi, and Branislav Kveton. Bayesian fixed-budget best-arm identification, 2023. a rXiv:2211.08572

    2023 arXiv

  2. [10]

    Minimax policies for adversarial and stochastic bandits

    Jean - Yves Audibert and S \' e bastien Bubeck. Minimax policies for adversarial and stochastic bandits. In Conference on Learning Theory (COLT), 2009

    2009

  3. [11]

    Best arm identification in multi-armed bandits

    Jean-Yves Audibert, S \'e bastien Bubeck, and Remi Munos. Best arm identification in multi-armed bandits. In Conference on Learning Theory, pp.\ 41--53, 2010

    2010

  4. [12]

    Pure exploration in finitely-armed and continuous-armed bandits

    S \'e bastien Bubeck, R \'e mi Munos, and Gilles Stoltz. Pure exploration in finitely-armed and continuous-armed bandits. Theoretical Computer Science, 2011

    2011

  5. [13]

    Distribution Function Inequalities for Martingales

    Donald Lyman Burkholder. Distribution Function Inequalities for Martingales . The Annals of Probability, 1 0 (1): 0 19 -- 42, 1973

    1973

  6. [14]

    Burnetas and Michael N

    Apostolos N. Burnetas and Michael N. Katehakis. Optimal adaptive policies for sequential allocation problems. Advances in Applied Mathematics, 17 0 (2): 0 122--142, 1996

    1996

  7. [15]

    On the performance of the neyman allocation with small pilots

    Yong Cai and Ahnaf Rafi. On the performance of the neyman allocation with small pilots. Journal of Econometrics, 242 0 (1), 2024

    2024

  8. [16]

    Geometric Modeling in Probability and Statistics

    Ovidiu Calin and Constantin Udrişte. Geometric Modeling in Probability and Statistics. Mathematics and Statistics. Springer International Publishing, 2014

    2014

  9. [17]

    Tight (lower) bounds for the fixed budget best arm identification bandit problem

    Alexandra Carpentier and Andrea Locatelli. Tight (lower) bounds for the fixed budget best arm identification bandit problem. In COLT, 2016

    2016

  10. [18]

    An effective approach to smartly allocate computing budget for discrete event simulation

    Chun-Hung Chen. An effective approach to smartly allocate computing budget for discrete event simulation. In IEEE Conference on Decision and Control, 1995

    1995

  11. [19]

    Chun-Hung Chen, Jianwu Lin, Enver Y\" u cesan, and Stephen E. Chick. Simulation budget allocation for further enhancing the efficiency of ordinal optimization. Discrete Event Dynamic Systems, 10 0 (3): 0 251--270, 2000

    2000

  12. [20]

    Semiparametric efficient inference in adaptive experiments

    Thomas Cook, Alan Mishler, and Aaditya Ramdas. Semiparametric efficient inference in adaptive experiments. In Conference on Causal Learning and Reasoning, 2024

    2024

  13. [21]

    CLIP - OGD : An experimental design for adaptive neyman allocation in sequential experiments

    Jessica Dai, Paula Gradu, and Christopher Harshaw. CLIP - OGD : An experimental design for adaptive neyman allocation in sequential experiments. In Conference on Neural Information Processing Systems (NeurIPS), 2023

    2023

  14. [22]

    On the existence of a complexity in fixed budget bandit identification

    R \'e my Degenne. On the existence of a complexity in fixed budget bandit identification. In Conference on Learning Theory, volume 195, pp.\ 1131--1154. PMLR, 2023

    2023

  15. [23]

    Lecture notes on statistics and information theory, 2023

    John Duchi. Lecture notes on statistics and information theory, 2023. URL https://web.stanford.edu/class/stats311/lecture-notes.pdf

    2023

  16. [24]

    Adaptive Experiments for Policy Choice : Phone Calls for Home Reading in Kenya

    Bruno Nicola Esposito Acosta and Anja Sautmann. Adaptive Experiments for Policy Choice : Phone Calls for Home Reading in Kenya . Policy Research Working Paper Series 10098, The World Bank, June 2022. URL https://ideas.repec.org/p/wbk/wbrwps/10098.html

    2022

  17. [25]

    Adaptive designs for clinical trials of drugs and biologics: Guidance for industry

    FDA. Adaptive designs for clinical trials of drugs and biologics: Guidance for industry. Technical report, U.S. Department of Health and Human Services Food and Drug Administration (FDA), Center for Drug Evaluation and Research (CDER), Center for Biologics Evaluation and Resea...

    2019

  18. [26]

    Optimal best arm identification with fixed confidence

    Aur \'e lien Garivier and Emilie Kaufmann. Optimal best arm identification with fixed confidence. In Conference on Learning Theory, 2016

    2016

  19. [27]

    John C. Gittins. Multi-armed Bandit Allocation Indices. Wiley, Chichester, NY, 1989

    1989

  20. [28]

    A large deviations perspective on ordinal optimization

    Peter Glynn and Sandeep Juneja. A large deviations perspective on ordinal optimization. In Proceedings of the 2004 Winter Simulation Conference, volume 1. IEEE, 2004

    2004

  21. [29]

    Adaptive experimental design using the propensity score

    Jinyong Hahn, Keisuke Hirano, and Dean Karlan. Adaptive experimental design using the propensity score. Journal of Business & Economic Statistics, 29 0 (1): 0 96--108, 2011

    2011

  22. [30]

    Martingale Limit Theory and Its Application

    Peter Hall and Christopher Charles Heyde. Martingale Limit Theory and Its Application. Communication and Behavior. Academic Press, 2014

    2014

  23. [31]

    Econometrics

    Fumio Hayashi. Econometrics. Princeton Univ. Press, 2000

    2000

  24. [32]

    Econometrics: Typo\/error alert, 2010

    Fumio Hayashi. Econometrics: Typo\/error alert, 2010. URL http://fhayashi.fc2web.com/hayashi\

    2010

  25. [33]

    Keisuke Hirano and Jack R. Porter. Asymptotics for statistical treatment rules. Econometrica, 77 0 (5): 0 1683--1701, 2009

    2009

  26. [34]

    Keisuke Hirano and Jack R. Porter. Asymptotic representations for sequential decisions, adaptive experiments, and batched bandits, 2025. URL https://arxiv.org/abs/2302.03117

    2025 arXiv

  27. [35]

    Imbens and Donald B

    Guido W. Imbens and Donald B. Rubin. Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction. Cambridge University Press, 2015

    2015

  28. [36]

    Imbens, Chao Qin, and Stefan Wager

    Guido W. Imbens, Chao Qin, and Stefan Wager. Admissibility of completely randomized trials: A large-deviation approach, 2025. a rXiv: 2506.05329

    2025 arXiv

  29. [37]

    Double reinforcement learning for efficient off-policy evaluation in markov decision processes

    Nathan Kallus and Masatoshi Uehara. Double reinforcement learning for efficient off-policy evaluation in markov decision processes. Journal of Machine Learning Research, 21 0 (1), 2020

    2020

  30. [38]

    Karlan and Jonathan Zinman

    Dean S. Karlan and Jonathan Zinman. Observing Unobservables: Identifying Information Asymmetries with a Consumer Credit Field Experiment . Center Discussion Papers 28482, Yale University, Economic Growth Center, 2005

    2005

  31. [39]

    Adaptive treatment assignment in experiments for policy choice

    Maximilian Kasy and Anja Sautmann. Adaptive treatment assignment in experiments for policy choice. Econometrica, 89 0 (1): 0 113--132, 2021 a

    2021

  32. [40]

    adaptive treatment assignment in experiments for policy choice

    Maximilian Kasy and Anja Sautmann. Correction regarding “adaptive treatment assignment in experiments for policy choice”, 2021 b . URL https://maxkasy.github.io/home/files/papers/correction_adaptiveexperimentspolicy.pdf

    2021

  33. [41]

    Generalized N eyman allocation for locally minimax optimal best-arm identification, 2024

    Masahiro Kato. Generalized N eyman allocation for locally minimax optimal best-arm identification, 2024. a rXiv: 2405.19317

    2024 arXiv

  34. [42]

    Neyman allocation for two-armed gaussian best-arm identification with unknown variances

    Masahiro Kato. Neyman allocation for two-armed gaussian best-arm identification with unknown variances. In IIAI International Congress on Advanced Applied Informatics (IIAI-AAI), 2025

    2025

  35. [43]

    The role of contextual information in best arm identification, 2021

    Masahiro Kato and Kaito Ariu. The role of contextual information in best arm identification, 2021

    2021

  36. [44]

    Efficient adaptive experimental design for average treatment effect estimation, 2020

    Masahiro Kato, Takuya Ishihara, Junya Honda, and Yusuke Narita. Efficient adaptive experimental design for average treatment effect estimation, 2020. a rXiv:2002.05308

    2020 arXiv

  37. [45]

    The adaptive doubly robust estimator and a paradox concerning logging policy

    Masahiro Kato, Kenichiro McAlinn, and Shota Yasui. The adaptive doubly robust estimator and a paradox concerning logging policy. In International Conference on Neural Information Processing Systems (NeurIPS), 2021

    2021

  38. [46]

    Asymptotically optimal fixed-budget best arm identification with variance-dependent bounds, 2023 a

    Masahiro Kato, Masaaki Imaizumi, Takuya Ishihara, and Toru Kitagawa. Asymptotically optimal fixed-budget best arm identification with variance-dependent bounds, 2023 a . a rXiv: 2302.02988

    2023 arXiv

  39. [47]

    Best arm identification with contextual information under a small gap, 2023 b

    Masahiro Kato, Masaaki Imaizumi, Takuya Ishihara, and Toru Kitagawa. Best arm identification with contextual information under a small gap, 2023 b . a rXiv: 2209.07330

    2023 arXiv

  40. [48]

    Fixed-budget hypothesis best arm identification: On the information loss in experimental design

    Masahiro Kato, Masaaki Imaizumi, Takuya Ishihara, and Toru Kitagawa. Fixed-budget hypothesis best arm identification: On the information loss in experimental design. In ICML Workshop on New Frontiers in Learning, Control, and Dynamical Systems, 2023 c

    2023

  41. [49]

    Active adaptive experimental design for treatment effect estimation with covariate choice

    Masahiro Kato, Akihiro Oga, Wataru Komatsubara, and Ryo Inokuchi. Active adaptive experimental design for treatment effect estimation with covariate choice. In International Conference on Machine Learning (ICML), 2024 a

    2024

  42. [50]

    Adaptive experimental design for policy learning, 2024 b

    Masahiro Kato, Kyohei Okumura, Takuya Ishihara, and Toru Kitagawa. Adaptive experimental design for policy learning, 2024 b . a rXiv: 2401.03756

    2024 arXiv

  43. [51]

    Contributions to the Optimal Solution of Several Bandits Problems

    Emilie Kaufmann. Contributions to the Optimal Solution of Several Bandits Problems. Habilitation \` a Diriger des Recherches, Universit\' e de Lille, 2020. URL https://emiliekaufmann.github.io/HDR_EmilieKaufmann.pdf

    2020

  44. [52]

    On the complexity of a/b testing

    Emilie Kaufmann, Olivier Capp \'e , and Aur \'e lien Garivier. On the complexity of a/b testing. In Conference on Learning Theory, volume 35, pp.\ 461--481, 2014

    2014

  45. [53]

    On the complexity of best-arm identification in multi-armed bandit models

    Emilie Kaufmann, Olivier Capp \'e , and Aur \'e lien Garivier. On the complexity of best-arm identification in multi-armed bandit models. Journal of Machine Learning Research, 17 0 (1): 0 1--42, 2016

    2016

  46. [54]

    Who should be treated? empirical welfare maximization methods for treatment choice

    Toru Kitagawa and Aleksey Tetenov. Who should be treated? empirical welfare maximization methods for treatment choice. Econometrica, 86 0 (2): 0 591--616, 2018

    2018

  47. [55]

    A policy gradient primal-dual algorithm for constrained mdps with uniform pac guarantees, 2024

    Toshinori Kitamura, Tadashi Kozuno, Masahiro Kato, Yuki Ichihara, Soichiro Nishimori, Akiyoshi Sannai, Sho Sonoda, Wataru Kumagai, and Yutaka Matsuo. A policy gradient primal-dual algorithm for constrained mdps with uniform pac guarantees, 2024. a rXiv: 2401.17780

    2024 arXiv

  48. [56]

    Minimax optimal algorithms for fixed-budget best arm identification

    Junpei Komiyama, Taira Tsuchiya, and Junya Honda. Minimax optimal algorithms for fixed-budget best arm identification. In Advances in Neural Information Processing Systems, 2022

    2022

  49. [57]

    Rate-optimal bayesian simple regret in best arm identification

    Junpei Komiyama, Kaito Ariu, Masahiro Kato, and Chao Qin. Rate-optimal bayesian simple regret in best arm identification. Mathematics of Operations Research, 2023

    2023

  50. [58]

    Adaptive Treatment Allocation and the Multi-Armed Bandit Problem

    Tze Leung Lai. Adaptive Treatment Allocation and the Multi-Armed Bandit Problem . The Annals of Statistics, 15 0 (3): 0 1091 -- 1114, 1987

    1987

  51. [59]

    Asymptotically efficient adaptive allocation rules

    Tze Leung Lai and Herbert Robbins. Asymptotically efficient adaptive allocation rules. Advances in Applied Mathematics, 6 0 (1): 0 4--22, 1985

    1985

  52. [60]

    Charles F. Manski. Identification problems and decisions under ambiguity: Empirical analysis of treatment response and normative analysis of treatment choice. Journal of Econometrics, 95 0 (2): 0 415--442, 2000

    2000

  53. [61]

    Charles F. Manski. Treatment choice under ambiguity induced by inferential problems. Journal of Statistical Planning and Inference, 105 0 (1): 0 67--82, 2002

    2002

  54. [62]

    Charles F. Manski. Statistical treatment rules for heterogeneous populations. Econometrica, 72 0 (4): 0 1221--1246, 2004

    2004

  55. [63]

    Open problem: Finite-time instance dependent optimality for stochastic online learning with feedback graphs

    Teodor Vanislavov Marinov, Mehryar Mohri, and Julian Zimmert. Open problem: Finite-time instance dependent optimality for stochastic online learning with feedback graphs. In Conference on Learning Theory (COLT), 2022

    2022

  56. [64]

    Susan A. Murphy. Optimal dynamic treatment regimes. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65 0 (2): 0 331--355, 2003

    2003

  57. [65]

    Logarithmic neyman regret for adaptive estimation of the average treatment effect, 2024

    Ojash Neopane, Aaditya Ramdas, and Aarti Singh. Logarithmic neyman regret for adaptive estimation of the average treatment effect, 2024. a rXiv: 2411.14341

    2024 arXiv

  58. [66]

    Prior-dependent allocations for bayesian fixed-budget best-arm identification in structured bandits

    Nicolas Nguyen, Imad Aouali, Andr \'a s Gy \"o rgy, and Claire Vernade. Prior-dependent allocations for bayesian fixed-budget best-arm identification in structured bandits. In International Conference on Artificial Intelligence and Statistics (AISTATS), 2025

    2025

  59. [67]

    Stronger neyman regret guarantees for adaptive experimental design, 2025

    Georgy Noarov, Riccardo Fogliato, Martin Bertran, and Aaron Roth. Stronger neyman regret guarantees for adaptive experimental design, 2025. a rXiv: 2502.17427

    2025 arXiv

  60. [68]

    Open problem: Optimal best arm identification with fixed-budget

    Chao Qin. Open problem: Optimal best arm identification with fixed-budget. In Conference on Learning Theory, 2022

    2022

  61. [69]

    Efficient semiparametric estimation of average treatment effects under covariate adaptive randomization, 2023

    Ahnaf Rafi. Efficient semiparametric estimation of average treatment effects under covariate adaptive randomization, 2023. a rXiv:2305.08340

    2023 arXiv

  62. [70]

    Simple bayesian algorithms for best-arm identification

    Daniel Russo. Simple bayesian algorithms for best-arm identification. Operations Research, 68 0 (6): 0 1625--1647, 2020

    2020

  63. [71]

    Policy learning for optimal dynamic treatment regimes with observational data, 2025

    Shosei Sakaguchi. Policy learning for optimal dynamic treatment regimes with observational data, 2025. a rXiv: 2404.00221

    2025 arXiv

  64. [72]

    Statistical consideration of adaptive methods in clinical development

    Annpey Pong Shein-Chung Chow, Mark Chang. Statistical consideration of adaptive methods in clinical development. Journal of Biopharmaceutical Statistics, 2005

    2005

  65. [73]

    Charles J. Stone. Optimal global rates of convergence for nonparametric regression. The Annals of Statistics, 10 0 (4): 0 1040--1053, 1982

    1982

  66. [74]

    Batch learning from logged bandit feedback through counterfactual risk minimization

    Adith Swaminathan and Thorsten Joachims. Batch learning from logged bandit feedback through counterfactual risk minimization. Journal of Machine Learning Research, 16 0 (52): 0 1731--1755, 2015

    2015

  67. [75]

    On the likelihood that one unknown probability exceeds another in view of the evidence of two samples

    William R Thompson. On the likelihood that one unknown probability exceeds another in view of the evidence of two samples. Biometrika, 25 0 (3-4): 0 285--294, 12 1933

    1933

  68. [76]

    van der Laan

    Mark J. van der Laan. The construction and analysis of adaptive group sequential designs, 2008. URL https://biostats.bepress.com/ucbbiostat/paper232/

    2008

  69. [77]

    van der Vaart

    Aad W. van der Vaart. Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, 1998

    1998

  70. [78]

    Statistical Decision Functions

    Abraham Wald. Statistical Decision Functions. Wiley: New York, 1950

    1950

  71. [79]

    On uniformly optimal algorithms for best arm identification in two-armed bandits with fixed budget

    Po-An Wang, Kaito Ariu, and Alexandre Proutiere. On uniformly optimal algorithms for best arm identification in two-armed bandits with fixed budget. In International Conference on Machine Learning (ICML), 2024

    2024

  72. [80]

    Offline multi-action policy learning: Generalization and optimization

    Zhengyuan Zhou, Susan Athey, and Stefan Wager. Offline multi-action policy learning: Generalization and optimization. Operations Research, 71 0 (1): 0 148--183, 2023

    2023

  73. [81]

    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 gl...

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.