Pith. sign in

REVIEW 3 major objections 4 minor 60 references

Treating observational conditional probability tables as the unknown parameter lets one intervention's data update another's reward estimates, giving information-directed sampling sublinear Bayesian regret.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-01 22:52 UTC pith:MRQGZXAF

load-bearing objection Solid TS regret bound for causal bandits with non-manipulable variables, but the IDS MC-error claim is conditional and under-specified—worth refereeing. the 3 major comments →

arxiv 2607.15577 v1 pith:MRQGZXAF submitted 2026-07-17 cs.LG cs.AI

Information-Directed Sampling for Causal Bandits

Muhammad Qasim Elahi , Murat Kocaoglu , Mahsa Ghasemi This is my paper
classification cs.LG cs.AI
keywords causal banditsnon-manipulable variablesinformation-directed samplingBayesian regretconditional probability tablescontextual banditscausal graphsposterior sampling
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper studies sequential decisions about which variables to intervene on when some variables cannot be manipulated but still affect the reward. The central move is to make the unknown object the conditional probability tables of the observational distribution, rather than the rewards of individual arms. Because those tables are shared across interventions, an observation gathered under one intervention updates the estimated rewards of other interventions that use the same mechanisms. The paper proves that information-directed sampling in this setting has sublinear Bayesian regret — of order sqrt(|A| T H(Π*)) with exact information ratios — and that a Monte Carlo version retains the same rate up to an explicit approximation-error term. This matters because it gives a formal guarantee for a common practical situation where context and outcome variables are observed but not manipulable.

Core claim

Under the assumptions of a known causal graph with no latent confounders, the paper establishes that the cumulative Bayesian regret of its information-directed sampling algorithm is at most sqrt(|A| T H(Π*)/2) when the information ratio can be computed exactly, and at most sqrt(H(Π*)(T|A|/2 + 2 Σ_t γ_t)) when information ratios are estimated by Monte Carlo, with high probability. The corresponding posterior-sampling algorithm achieves sqrt(T |A| |C| log|A| / 2). The mechanism is a conjugate Dirichlet posterior over the conditional probability tables: each round contributes counts (V_i, Pa_i) for every non-intervened variable, so the posterior is shared and every intervention refines beliefs

What carries the argument

The load-bearing object is the vector θ of conditional probability tables of the observational distribution. Because the graph is assumed free of latent confounders, the truncated factorization formula expresses every intervention's expected reward as a function of θ, so a single posterior over θ serves all arms. A Dirichlet prior with counts updated by (3) — counting each observed (V_i, Pa_i) pair only when the action does not intervene on V_i — is the mechanism that transfers information across interventions. For IDS, the information ratio Δ_t(π|c_t)^2 / g_t(π|c_t), with g_t the mutual information about the optimal action under the current context, is what the algorithm minimizes; H(Π*) bo

Load-bearing premise

The load-bearing premise is that after every intervention the agent observes the reward and all non-intervened variables; if some of those variables are unobservable, the Dirichlet count update that carries information across interventions cannot be applied.

What would settle it

Take a graph X→Y with non-manipulable X, run Algorithm 2 with reward-only feedback (suppress the post-intervention observation of X), and track cumulative regret against the claimed sqrt(|A| T H(Π*)/2) bound. If the regret grows linearly, or if the count N_ijk in equation (3) is undefined because the non-intervened variable is never seen, the shared-information mechanism and the bound fail.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • If the causal graph and full observability hold, regret grows only as sqrt(T), so exploration effort is shared across interventions instead of being spent on each arm independently.
  • The leading constant in the regret bound is governed by H(Π*), the prior entropy over optimal action mappings, which can be smaller than the worst-case log|A|; the paper's example shows an 8.7% reduction in the leading coefficient.
  • With Monte Carlo estimation of information ratios, the regret bound degrades by an explicit additive term 2 Σ_t γ_t that shrinks as the number of posterior samples N grows.
  • In finite context spaces, the posterior-sampling variant attains sqrt(T |A| |C| log|A| / 2), giving a concrete sublinear guarantee for the non-manipulable-variable setting.
  • On the paper's synthetic and randomly generated chordal graphs, both proposed algorithms achieve lower cumulative regret than the non-causal baselines.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • My inference: the full-observability assumption is the real boundary of the result; if only the reward is observed, the Dirichlet counts in (3) cannot be formed, and a different mechanism (e.g., estimating missing parent configurations) would be needed to retain the bound.
  • My inference: the entropy-dependent bound suggests a practical diagnostic — compute H(Π*) from prior samples before deployment; a concentrated prior predicts a smaller regret coefficient, as the paper's own example illustrates.
  • My inference: the same posterior-over-CPTs formulation could extend to partially observed non-intervened variables by maintaining a posterior over missing configurations, but the concentration proofs would need new machinery; the paper does not address this.
  • My inference: the information-ratio decomposition suggests that in graphs with strong shared mechanisms, exploration should favor interventions that directly reveal rare parent configurations of reward, rather than the observational action, even though do() samples the natural distribution.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper studies contextual causal bandits with non-manipulable variables under a known causal graph without latent confounding. The unknown parameter is the collection of conditional probability tables of the observational distribution, and the posterior is updated Dirichlet-by-Dirichlet from observations of the reward and all non-intervened variables after each intervention. Two algorithms are proposed: a causal Thompson Sampling (Algorithm 1) and an Information-Directed Sampling variant (Algorithm 2) that approximates the IDS objective by Monte Carlo. The main theoretical claims are an entropy-dependent sublinear Bayesian regret bound for TS (Theorem 1, Corollary 1), an oracle IDS bound recovering the standard rate (Corollary 2), and an IDS regret bound that explicitly accounts for Monte Carlo approximation error (Theorem 2). Experiments on structured and randomly generated causal graphs compare the proposed algorithms with UCB, Bernoulli TS, and the Lee–Bareinboim z2ID baseline.

Significance. If correct, the paper provides a clean Bayesian treatment of intervention sharing through shared conditional probability tables in causal bandits, and it gives the first regret analyses for this specific formulation with non-manipulable variables. The TS analysis (Theorem 1/Corollary 1) and the oracle IDS analysis (Corollary 2) are standard and, on inspection, sound; they are useful contributions. The paper also attempts to quantify the effect of Monte Carlo approximation in IDS, which is a practically important and non-obvious extension. However, the advertised MC-aware guarantee in Theorem 2 is not established as an unconditional Bayesian regret bound, and the quantity γ_t is not an explicit bound. These issues are load-bearing for the stated contribution. The empirical comparison may also be confounded if the baselines do not receive the same post-intervention observations.

major comments (3)
  1. [Theorem 2, Appendix A.8 (Eqs. (48), (66), (67))] The advertised MC-aware regret guarantee is not established as stated. The proof derives only the conditional inequality Ψ_t(π̂_t|c_t) ≤ |A|/2 + 2γ_t on the Monte Carlo confidence event E (Eq. (66)), then substitutes this into Eq. (48), which is an unconditional expectation. By the law of total expectation, E[Reg] = P(E)E[Reg|E] + P(E^c)E[Reg|E^c]; the proof supplies no control on E[Reg|E^c] and no integrable bound on γ_t, so Eq. (9) cannot be read as an unconditional Bayesian regret bound. The parenthetical 'conditional on the Monte Carlo confidence event' confirms this. Since quantifying Monte Carlo error is a central claimed contribution, the statement must either be revised to a conditional bound with explicit notation, or supplemented with a tail term (e.g., δ′T) to obtain an unconditional regret bound.
  2. [Eq. (10), Theorem 2] γ_t is defined as a supremum over confidence sets and has no explicit rate. The widths O(sqrt(log(c/δ)/N)) of individual intervals do not imply a rate for γ_t without quantitative control on the ratio function over the confidence set; denominators may approach zero. The claim that the bound 'explicitly quantifies' the additional Monte Carlo error is therefore unsupported. Please provide an explicit upper bound on γ_t (or on Σ_t γ_t) in terms of N, δ′, |A|, and problem constants, or a computable bound that can actually be evaluated by the algorithm.
  3. [Section 7, Figures 3–4] The empirical comparison appears potentially confounded. The baselines are described as non-causal UCB, Bernoulli TS, and the Lee–Bareinboim z2ID method, but the paper does not state whether these baselines receive the same post-intervention observations (reward plus all non-intervened variables) as the proposed algorithms. If the baselines have access only to rewards, the proposed algorithms' advantage may be due to extra feedback rather than to the TS/IDS exploration strategy. Please specify the observation model for every algorithm and, if the feedback differs, either compare under identical feedback or clearly state and justify the difference.
minor comments (4)
  1. [Section 4, Eq. (3); Algorithm 1] The posterior update and all regret bounds rely on observing the reward and all non-intervened variables after each intervention. This is stronger than the usual bandit feedback and should be stated prominently as a central assumption/limitation, with a discussion of whether any part of the analysis survives when only the reward is observed.
  2. [Theorem 2 statement] The statement says 'with probability at least 1−δ′ over the Monte Carlo samples, the Bayesian regret satisfies ...' but the displayed expectation is not explicitly conditional on the Monte Carlo confidence event. Please use E[·|E] or otherwise clarify that the bound is conditional, and spell out the implications for the unconditional regret.
  3. [Lemma 4 / Section A.7] The lower confidence bound g_t(a|c_t) is defined as the optimum of a convex program (35). The paper only says it is solved with a standard solver; no computational complexity, numerical tolerance, or guarantee that the solver returns the exact optimum is given. This is a practical gap, especially because Algorithm 2 relies on these bounds at every round.
  4. [Section 5, Theorem 1 / Corollary 1] The entropy H(Π*) of the optimal mapping is used without explicitly defining it for uncountable context spaces; Corollary 1 assumes finite C, but the general theorem should state finiteness or use a differential/integral definition.

Circularity Check

0 steps flagged

No material circularity: bounds are derived from stated Bayesian assumptions and standard external frameworks; the MC-error term is a definitional bound, not a fitted prediction.

full rationale

The derivation chain is self-contained. The TS bound (Theorem 1 / Corollary 1) follows the Russo-Van Roy information-ratio argument: per-round regret is bounded by Γ_t times the square root of filtered mutual information, the information gain telescopes to H(Π⋆), a prior quantity over the optimal-action mapping, and the |A|/2 bound on Γ_t is proved in Appendix A.3 from posterior matching, Pinsker's inequality, and Cauchy-Schwarz. No target regret value is fed into the argument. The POMIS reduction is imported from Lee and Bareinboim (external authors), and causal identifiability is the standard truncated factorization under no latent confounding. For IDS, Lemmas 3-4 are Hoeffding-style concentration bounds over i.i.d. posterior samples; the γ_t term in Theorem 2 is defined as the worst-case information-ratio gap over the same confidence sets used by Algorithm 2, so bounding the approximation error by 2Σγ_t is a definitional bound rather than a fitted-input-called-prediction. Self-citations (Qasim Elahi et al. 2024, Wei et al. 2024, Squires et al. 2020) are contextual or experimental-generation references and are not load-bearing. One non-circular limitation is flagged: Theorem 2's bound is stated 'conditional on the Monte Carlo confidence event', and the proof substitutes event-level inequality (66) into expectation (48); this is a correctness/quantification concern for the unconditional regret claim, not a circularity, so it does not increase the circularity score.

Axiom & Free-Parameter Ledger

3 free parameters · 6 axioms · 0 invented entities

No free parameters are fit to data; the listed parameters are algorithm/prior choices. The assumptions are standard causal/Bayesian modeling choices, all stated in the paper. The theoretical claims rest mainly on prior work by Russo and Van Roy and Lee and Bareinboim.

free parameters (3)
  • posterior sample size N = 1000 (experiments)
    Controls Monte Carlo error in Lemmas 3 and 4 and the γ_t term in Theorem 2; chosen by hand, not data-fitted.
  • prior pseudocounts α_ijk = Beta(1,1) in the illustrative example; unspecified in experiments
    Dirichlet prior hyperparameters; not fitted to data but affect H(Π⋆) and thus the regret constant.
  • confidence level δ′ = not specified
    Input to Algorithm 2; controls the probability that the regret bound holds. Chosen by hand.
axioms (6)
  • domain assumption The causal graph G is known and has no latent confounders
    Used throughout; enables truncated-factorization identification and direct Dirichlet updates (Sections 2 and 4).
  • domain assumption The reward and all non-intervened variables are observed after each intervention
    Needed for the N_ijk counts in Eq. (3); if observation is partial, the posterior update and information sharing break.
  • domain assumption Context C is closed under ancestry, An(C)=C
    Assumed so interventions cannot affect context variables (Section 2).
  • domain assumption Parameter independence across local conditional distributions θ_ij with Dirichlet priors
    Gives the product posterior in Eq. (2); a modeling choice, not implied by the causal graph.
  • standard math Lee and Bareinboim's POMIS projection result gives the possibly optimal minimal intervention sets for the non-manipulable problem
    Cited from [Lee and Bareinboim 2019]; the action set A used by all algorithms is built on it.
  • standard math Russo and Van Roy's information-ratio analysis, including the worst-case Γ² ≤ |A|/2 bound
    The TS and oracle-IDS regret bounds are direct applications of Russo and Van Roy [2014, 2016].

pith-pipeline@v1.3.0-alltime-deepseek · 21666 in / 15068 out tokens · 167996 ms · 2026-08-01T22:52:27.850447+00:00 · methodology

0 comments
read the original abstract

Causal bandits exploit structural relationships among variables to share information across interventions and accelerate the identification of high-reward decisions. In many applications, however, some variables cannot be directly manipulated, even though they influence the reward and provide useful information about the underlying causal system. We study contextual causal bandits with non-manipulable variables, where context variables are observed before action selection and additional variables are observed after each intervention. Assuming a known causal graph without latent confounding, we adopt a Bayesian formulation in which the conditional probability tables of the observational distribution constitute the unknown parameter. This representation allows observations collected under one intervention to update reward estimates for other interventions through their shared causal mechanisms. We develop causal variants of Thompson Sampling and Information-Directed Sampling (IDS) for this setting. For Thompson Sampling, we establish an entropy-dependent sublinear Bayesian regret bound. For IDS, we derive an entropy-dependent regret bound that explicitly quantifies the additional error introduced by Monte Carlo approximation of the expected regret and information gain; when these quantities are available exactly, the bound recovers the standard sublinear IDS rate. We further provide high-probability confidence bounds for the Monte Carlo estimates used by the algorithm. Experiments on several synthetic causal bandit tasks show that the proposed methods outperform causal and non-causal baselines by more effectively exploiting information shared across interventions.

Figures

Figures reproduced from arXiv: 2607.15577 by Mahsa Ghasemi, Muhammad Qasim Elahi, Murat Kocaoglu.

Figure 1
Figure 1. Figure 1: Original causal graphs G1 and G2, along with their projections H1 and H2. For a causal graph G in which all nodes except the reward node Y are manipulable, we use the notation PG,Y to denote the collection of all POMISs. In the more general setting where the variables in N cannot be intervened upon, we use P N G,Y to denote the corresponding collection of possibly optimal minimal intervention sets. Followi… view at source ↗
Figure 2
Figure 2. Figure 2: Causal graphs used in the experiments same causal mechanisms and shared conditional probability tables. Thus, the causal model induces a joint prior over the intervention rewards and, consequently, a prior distribution over the optimal intervention Π⋆ . Assuming no prior observations, we place independent Beta(1, 1) priors on the Bernoulli parameters in each row of the conditional probability tables and es… view at source ↗
Figure 3
Figure 3. Figure 3: Regret versus time for the three tasks with the corresponding causal graphs shown in Figure 2 [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Regret versus time for Erdős–Rényi random chordal graphs with varying graph density [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Experimental results for a causal graph motivated by a real-world healthcare scenario. [PITH_FULL_IMAGE:figures/full_fig_p026_5.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

60 extracted references · 3 linked inside Pith

  1. [1]

    Zur Elektrodynamik bewegter Körper

    Albert Einstein. Zur Elektrodynamik bewegter Körper. Annalen der Physik. 1905

    1905

  2. [2]

    The \ Companion

    Michel Goossens and Frank Mittelbach and Alexander Samarin. The \ Companion. 1993

    1993

  3. [3]

    Langley , title =

    P. Langley , title =. Proceedings of the 17th International Conference on Machine Learning (ICML 2000) , address =. 2000 , pages =

    2000

  4. [4]

    Aaai/iaai , pages=

    A general identification condition for causal effects , author=. Aaai/iaai , pages=

  5. [5]

    T. M. Mitchell. The Need for Biases in Learning Generalizations. 1980

    1980

  6. [6]

    M. J. Kearns , title =

  7. [7]

    Machine Learning: An Artificial Intelligence Approach, Vol. I. 1983

    1983

  8. [8]

    R. O. Duda and P. E. Hart and D. G. Stork. Pattern Classification. 2000

    2000

  9. [9]

    Suppressed for Anonymity , author=

  10. [10]

    Newell and P

    A. Newell and P. S. Rosenbloom. Mechanisms of Skill Acquisition and the Law of Practice. Cognitive Skills and Their Acquisition. 1981

    1981

  11. [11]

    A. L. Samuel. Some Studies in Machine Learning Using the Game of Checkers. IBM Journal of Research and Development. 1959

    1959

  12. [12]

    Advances in Neural Information Processing Systems , volume =

    Yasin Abbasi-Yadkori and Dávid Pál and Csaba Szepesvári , title =. Advances in Neural Information Processing Systems , volume =

  13. [13]

    Conference on Artificial Intelligence and Statistics (AISTATS) , year =

    Yasin Abbasi-Yadkori and Dávid Pál and Csaba Szepesvári , title =. Conference on Artificial Intelligence and Statistics (AISTATS) , year =

  14. [14]

    Anantharam , title =

    Rajeev Agrawal and Demosthenis Teneketzis and V. Anantharam , title =. IEEE Transactions on Automatic Control , volume =

  15. [15]

    Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics , pages =

    Shipra Agrawal and Navin Goyal , title =. Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics , pages =

  16. [16]

    Proceedings of the 30th International Conference on Machine Learning (ICML) , pages =

    Shipra Agrawal and Navin Goyal , title =. Proceedings of the 30th International Conference on Machine Learning (ICML) , pages =

  17. [17]

    Proceedings of the 22nd Annual Conference on Learning Theory (COLT) , pages =

    Jean-Yves Audibert and Sébastien Bubeck , title =. Proceedings of the 22nd Annual Conference on Learning Theory (COLT) , pages =

  18. [18]

    Machine Learning , volume =

    Peter Auer and Nicolò Cesa-Bianchi and Paul Fischer , title =. Machine Learning , volume =

  19. [19]

    Machine Learning , volume=

    Finite-time analysis of the multiarmed bandit problem , author=. Machine Learning , volume=

  20. [20]

    The Annals of Statistics , volume=

    Kullback--Leibler upper confidence bounds for optimal sequential allocation , author=. The Annals of Statistics , volume=

  21. [21]

    Journal of Causal Inference , volume=

    Decision-theoretic foundations for statistical causality , author=. Journal of Causal Inference , volume=

  22. [22]

    UAI , pages=

    Constraint-based causal discovery: Conflict resolution with answer set programming , author=. UAI , pages=

  23. [23]

    Advances in Applied Mathematics , volume=

    Asymptotically efficient adaptive allocation rules , author=. Advances in Applied Mathematics , volume=

  24. [24]

    Advances in Neural Information Processing Systems , pages=

    Causal bandits: Learning good interventions via causal inference , author=. Advances in Neural Information Processing Systems , pages=

  25. [25]

    Advances in Neural Information Processing Systems 31 , pages=

    Structural causal bandits: Where to intervene? , author=. Advances in Neural Information Processing Systems 31 , pages=

  26. [26]

    Conference on Uncertainty in Artificial Intelligence , pages=

    Regret analysis of bandit problems with causal background knowledge , author=. Conference on Uncertainty in Artificial Intelligence , pages=

  27. [27]

    arXiv preprint arXiv:2106.02988 , year=

    Causal bandits with unknown graph structure , author=. arXiv preprint arXiv:2106.02988 , year=

    Pith/arXiv arXiv

  28. [28]

    Proceedings of Advances in Neural Information Processing Systems (NIPS 2016) , pages=

    Ancestral causal inference , author=. Proceedings of Advances in Neural Information Processing Systems (NIPS 2016) , pages=

    2016

  29. [29]

    Advances in Neural Information Processing Systems , pages=

    Domain adaptation by using causal inference to predict invariant conditional distributions , author=. Advances in Neural Information Processing Systems , pages=

  30. [30]

    Journal of Machine Learning Research , volume=

    Joint causal inference from multiple contexts , author=. Journal of Machine Learning Research , volume=. 2020 , url=

    2020

  31. [31]

    Learning Bayesian Networks , author=

  32. [32]

    Journal of the Royal Statistical Society: Series B (Statistical Methodology) , volume=

    Causal inference by using invariant prediction: Identification and confidence intervals , author=. Journal of the Royal Statistical Society: Series B (Statistical Methodology) , volume=

  33. [33]

    Journal of Machine Learning Research , volume=

    Invariant models for causal transfer learning , author=. Journal of Machine Learning Research , volume=

  34. [34]

    International Conference on Artificial Intelligence and Statistics , pages=

    A novel confidence-based algorithm for structured bandits , author=. International Conference on Artificial Intelligence and Statistics , pages=. 2020 , organization=

    2020

  35. [35]

    Advances in Neural Information Processing Systems , volume=

    Crush optimism with pessimism: Structured bandits beyond asymptotic optimality , author=. Advances in Neural Information Processing Systems , volume=

  36. [36]

    Cognitive psychology , volume=

    Finding structure in multi-armed bandits , author=. Cognitive psychology , volume=. 2020 , publisher=

    2020

  37. [37]

    Jamieson, Kevin and Malloy, Matthew and Nowak, Robert and Bubeck, S. lil’. Conference on Learning Theory , pages=. 2014 , organization=

    2014

  38. [38]

    2009 , publisher=

    Probabilistic graphical models: principles and techniques , author=. 2009 , publisher=

    2009

  39. [39]

    Advances in Neural Information Processing Systems , volume=

    Active structure learning of causal DAGs via directed clique trees , author=. Advances in Neural Information Processing Systems , volume=

  40. [40]

    Advances in Neural Information Processing Systems , volume=

    Approximate allocation matching for structural causal bandits with unobserved confounders , author=. Advances in Neural Information Processing Systems , volume=

  41. [41]

    arXiv e-prints , pages=

    Partial Structure Discovery is Sufficient for No-regret Learning in Causal Bandits , author=. arXiv e-prints , pages=

  42. [42]

    Garivier, Aur. The. Proceedings of the 24th annual conference on learning theory , pages=. 2011 , organization=

    2011

  43. [43]

    Science , volume=

    Causal protein-signaling networks derived from multiparameter single-cell data , author=. Science , volume=

  44. [44]

    arXiv preprint arXiv:1701.02789 , year=

    Identifying best interventions through online importance sampling , author=. arXiv preprint arXiv:1701.02789 , year=

    Pith/arXiv arXiv

  45. [45]

    Causation, Prediction, and Search , author=

  46. [46]

    Biometrika , volume=

    On the likelihood that one unknown probability exceeds another in view of the evidence of two samples , author=. Biometrika , volume=

  47. [47]

    arXiv preprint arXiv:1806.02252 , year=

    Causal bandits with propagating inference , author=. arXiv preprint arXiv:1806.02252 , year=

    Pith/arXiv arXiv

  48. [48]

    Advances in Neural Information Processing Systems , volume=

    Causal bandits with unknown graph structure , author=. Advances in Neural Information Processing Systems , volume=

  49. [49]

    Proceedings of the AAAI Conference on Artificial Intelligence , volume=

    Structural causal bandits with non-manipulable variables , author=. Proceedings of the AAAI Conference on Artificial Intelligence , volume=

  50. [50]

    Innovations in Machine Learning: Theory and Applications , pages=

    A Bayesian approach to causal discovery , author=. Innovations in Machine Learning: Theory and Applications , pages=. 2006 , publisher=

    2006

  51. [51]

    Journal of Machine Learning Research , volume=

    An information-theoretic analysis of thompson sampling , author=. Journal of Machine Learning Research , volume=

  52. [52]

    2020 , publisher=

    Bandit algorithms , author=. 2020 , publisher=

    2020

  53. [53]

    Foundations and Trends

    Introduction to multi-armed bandits , author=. Foundations and Trends. 2019 , publisher=

    2019

  54. [54]

    European conference on machine learning , pages=

    Multi-armed bandit algorithms and empirical evaluation , author=. European conference on machine learning , pages=. 2005 , organization=

    2005

  55. [55]

    2014 48th annual conference on information sciences and systems (CISS) , pages=

    Best-arm identification algorithms for multi-armed bandits in the fixed confidence setting , author=. 2014 48th annual conference on information sciences and systems (CISS) , pages=. 2014 , organization=

    2014

  56. [56]

    Advances in neural information processing systems , volume=

    Learning to optimize via information-directed sampling , author=. Advances in neural information processing systems , volume=

  57. [57]

    Management Science , volume=

    Optimal learning for structured bandits , author=. Management Science , volume=. 2024 , publisher=

    2024

  58. [58]

    International Conference on Artificial Intelligence and Statistics , pages=

    Towards scalable and robust structured bandits: A meta-learning framework , author=. International Conference on Artificial Intelligence and Statistics , pages=. 2023 , organization=

    2023

  59. [59]

    IEEE Transactions on Automatic Control , volume=

    A structured multiarmed bandit problem and the greedy policy , author=. IEEE Transactions on Automatic Control , volume=. 2009 , publisher=

    2009

  60. [60]

    International Conference on Machine Learning , pages=

    Best arm identification in linear bandits with linear dimension dependency , author=. International Conference on Machine Learning , pages=. 2018 , organization=

    2018