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arxiv: 2507.10797 · v2 · pith:ATXSP6G7new · submitted 2025-07-14 · 💻 cs.LG · math.OC· stat.ML

Multi-Armed Sampling Problem and the End of Exploration

Mohammad Pedramfar , Siamak Ravanbakhsh This is my paper

Pith reviewed 2026-05-19 04:09 UTC · model grok-4.3

classification 💻 cs.LG math.OCstat.ML
keywords multi-armed samplingregret boundsexploration-exploitationmulti-armed banditsreinforcement learningsampling algorithmstemperature parameterentropy-regularized RL
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The pith

Multi-armed sampling requires almost no exploration, unlike optimization in bandits.

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

This paper defines the multi-armed sampling problem as the sampling counterpart to the classic multi-armed bandit optimization task. It introduces specific notions of regret suited to sampling goals and proves matching lower bounds on performance. A simple algorithm is shown to attain near-optimal regret, which implies that deliberate exploration is largely unnecessary in this setting. A continuous family of problems parameterized by temperature unifies sampling with bandit problems, showing they form endpoints of the same spectrum. The results point to reduced emphasis on exploration in related areas such as entropy-regularized reinforcement learning and model fine-tuning.

Core claim

The central discovery is that sampling from a reward-derived distribution in the multi-armed setting can be performed with near-optimal regret using a straightforward algorithm that performs essentially no exploration. In contrast to multi-armed bandits, where exploration is essential for identifying high-reward arms, the lower bounds here establish that significant exploration does not improve asymptotic performance. The framework further shows that sampling and bandit problems are connected by a temperature parameter that interpolates between the two regimes.

What carries the argument

The regret notions defined specifically for multi-armed sampling, which measure deviation from the target sampling distribution rather than cumulative reward maximization.

Load-bearing premise

The chosen notions of regret for multi-armed sampling are the right measures for capturing the practical goals of sampling algorithms.

What would settle it

An empirical demonstration that a sampling algorithm incorporating explicit exploration outperforms the simple non-exploratory method on a downstream task whose success depends on sample quality would falsify the central claim.

Figures

Figures reproduced from arXiv: 2507.10797 by Mohammad Pedramfar, Siamak Ravanbakhsh.

Figure 1
Figure 1. Figure 1: Comparison between regret, specifically T.SART , of ASE and DAISEE with different statistical distances. From left to right, the distances are reverse-KL, forward-KL and total variation. Experiments for other notions are regret are included in the appendix. The initial increase in regret in the orange lines corresponds to the exploration phase (and its effect on action history). Environments have unit norm… view at source ↗
Figure 2
Figure 2. Figure 2: Action-level regret [PITH_FULL_IMAGE:figures/full_fig_p026_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Policy-level regret 26 [PITH_FULL_IMAGE:figures/full_fig_p026_3.png] view at source ↗
read the original abstract

This paper introduces the framework of multi-armed sampling, which serves as the sampling counterpart to the optimization problem of multi-armed bandits. Our primary motivation is to rigorously examine the exploration-exploitation trade-off in the context of sampling. We systematically define plausible notions of regret for this framework and establish corresponding lower bounds. We then propose a simple algorithm that achieves near-optimal regret bounds. Our theoretical results suggest that, in contrast to optimization, sampling barely requires any exploration. To further connect our findings with those of multi-armed bandits, we define a continuous family of problems and associated regret measures that smoothly interpolate and unify multi-armed sampling and multi-armed bandit problems using a temperature parameter. We believe that the multi-armed sampling framework and our findings in this setting can play a foundational role in the study of sampling, including recent neural samplers, much like the role of multi-armed bandits in reinforcement learning. In particular, our work sheds light on the role of exploration (or lack thereof) and the convergence properties of algorithms for entropy-regularized reinforcement learning, fine-tuning of pretrained models and reinforcement learning with human feedback (RLHF).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper introduces the multi-armed sampling framework as the sampling analog to multi-armed bandits. It systematically defines plausible regret notions for this setting, establishes corresponding lower bounds, and proposes a simple algorithm that achieves near-optimal regret. The central theoretical finding is that sampling requires barely any exploration, in contrast to optimization. The work further defines a continuous family of problems and regret measures, parameterized by a temperature, that interpolates between multi-armed sampling and multi-armed bandits, with implications for entropy-regularized RL, model fine-tuning, and RLHF.

Significance. If the chosen regret definitions prove to be the right measures for downstream sampling tasks, the result would be significant: it supplies a foundational theoretical lens for sampling algorithms analogous to the role of bandits in RL, and it offers a principled explanation for why exploration can be minimal in sampling contexts. The temperature-based unification is a clean technical contribution that could facilitate analysis of algorithms at the sampling end of the spectrum. The provision of lower bounds and a near-optimal simple algorithm strengthens the case for the framework's utility in studying neural samplers and RLHF.

major comments (1)
  1. The central claim that sampling barely requires exploration rests on the specific regret notions introduced for the multi-armed sampling problem. These notions must be shown to align with practical objectives such as accurate approximation of a target distribution (including mode coverage in multimodal cases) or effective sample quality. If the regrets instead emphasize average per-sample performance that can be optimized by concentrating on high-probability arms, the lower bounds and algorithm guarantees would not imply that minimal exploration suffices for typical sampling use cases. The manuscript should include an explicit discussion or comparison (e.g., to total-variation or effective-sample-size metrics) in the section defining the regrets.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive and insightful review. The major comment raises a valid point about explicitly connecting our regret definitions to practical sampling objectives. We address this below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: The central claim that sampling barely requires exploration rests on the specific regret notions introduced for the multi-armed sampling problem. These notions must be shown to align with practical objectives such as accurate approximation of a target distribution (including mode coverage in multimodal cases) or effective sample quality. If the regrets instead emphasize average per-sample performance that can be optimized by concentrating on high-probability arms, the lower bounds and algorithm guarantees would not imply that minimal exploration suffices for typical sampling use cases. The manuscript should include an explicit discussion or comparison (e.g., to total-variation or effective-sample-size metrics) in the section defining the regrets.

    Authors: We thank the referee for this important observation. Our regret notions for the multi-armed sampling problem are constructed to quantify cumulative deviation from the target distribution across repeated samples, which we believe captures key aspects of distribution approximation. We agree that an explicit discussion comparing these notions to total-variation distance, effective sample size, and implications for mode coverage would strengthen the presentation and help readers assess alignment with typical sampling use cases. We will add this discussion to the section defining the regrets in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

Regret definitions chosen by authors but core lower bounds and algorithm analysis remain first-principles derivations

full rationale

The paper defines new regret notions for the multi-armed sampling framework and derives lower bounds plus an algorithm achieving near-optimal performance directly from those definitions and standard concentration arguments. No step reduces a claimed prediction or uniqueness result to a fitted parameter or self-citation chain; the continuous temperature interpolation is constructed explicitly from the two endpoint problems rather than smuggled in. The only minor self-referential element is the authors' choice of which regret measures best capture sampling goals, which is acknowledged as an assumption rather than a load-bearing theorem. This keeps the overall circularity low while still noting that downstream relevance hinges on the chosen regrets.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The framework rests on standard assumptions about independent arm distributions and finite support or moments sufficient for regret analysis; no new entities are postulated and the temperature parameter is introduced as a modeling choice rather than fitted.

free parameters (1)
  • temperature parameter
    Continuous parameter that interpolates between sampling and bandit regimes; its specific values are chosen to recover the two extremes.
axioms (1)
  • domain assumption Arms are independent and each sample is drawn i.i.d. from its distribution.
    Standard assumption for multi-armed problems invoked to define sampling regret.

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Reference graph

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