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Instance-Dependent Fixed-Budget Pure Exploration in Reinforcement Learning

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 7.0Download Report PDF
Reinforcement LearningMDPpure explorationfixed budget
Abstract:

We study the problem of fixed budget pure exploration in reinforcement learning. The goal is to identify a near-optimal policy, given a fixed budget on the number of interactions with the environment. Unlike the standard PAC setting, we do not require the target error level ϵ\epsilon and failure rate δ\delta as input. We propose novel algorithms and provide, to the best of our knowledge, the first instance-dependent ϵ\epsilon-uniform guarantee, meaning that the probability that ϵ\epsilon-correctness is ensured can be obtained simultaneously for all ϵ\epsilon above a budget-dependent threshold. It characterizes the budget requirements in terms of the problem-specific hardness of exploration. As a core component of our analysis, we derive a ϵ\epsilon-uniform guarantee for the multiple bandit problem—solving multiple multi-armed bandit instances simultaneously—which may be of independent interest. To enable our analysis, we also develop tools for reward-free exploration under the fixed-budget setting, which we believe will be useful for future work.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper proposes the BREA algorithm for fixed-budget pure exploration in episodic MDPs, introducing the first instance-dependent ε-uniform guarantee that simultaneously ensures ε-correctness for all ε above a budget-dependent threshold. Within the taxonomy, it resides in the 'Episodic Fixed-Horizon MDP Pure Exploration' leaf, which contains only two papers total. This sparse population suggests the specific combination of fixed-budget constraints, episodic MDPs, and instance-dependent guarantees represents a relatively underexplored research direction compared to the more crowded multi-armed bandit branches.

The taxonomy reveals substantial activity in adjacent areas: the parent 'Episodic and Full MDP Pure Exploration' branch includes work on budgeted/constrained MDPs and reward-free exploration, while sibling branches address multi-armed bandits with various structural assumptions (combinatorial, linear, robust). The paper's positioning bridges classical episodic MDP exploration with instance-optimality concepts more commonly studied in bandit settings. Its scope explicitly targets episodic fixed-horizon problems, excluding infinite-horizon or continuous-state formulations, and distinguishes itself from the reward-free exploration work by maintaining a pure exploration objective rather than a preparatory phase.

Among the three identified contributions, the literature search examined nine candidates total with no clear refutations found. The BREA algorithm contribution examined three candidates with none providing overlapping prior work; similarly, the multiple bandit problem guarantee and fixed-budget reward-free tools each examined three candidates without refutation. This limited search scope (nine papers, not hundreds) means the analysis captures nearby semantic matches but cannot claim exhaustive coverage. The absence of refutations among these candidates suggests the specific technical contributions—particularly the ε-uniform guarantee formulation—may represent novel angles within the examined neighborhood.

Based on the top-nine semantic matches examined, the work appears to occupy a distinctive position combining fixed-budget constraints with instance-dependent analysis in episodic MDPs. The sparse taxonomy leaf and lack of refutations among examined candidates suggest novelty, though the limited search scope means potentially relevant work in broader RL theory or alternative formulations may exist outside this analysis. The multiple bandit subproblem and reward-free exploration tools appear to serve as technical enablers rather than standalone contributions with extensive prior literature.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
9
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: fixed-budget pure exploration in reinforcement learning. This field addresses the challenge of identifying optimal policies or states when an agent has a strict, predetermined budget of interactions with the environment. The taxonomy reveals a rich structure organized around problem formulations and methodological approaches. Multi-Armed Bandit Pure Exploration forms a foundational branch, encompassing classical best-arm identification and extensions to combinatorial, constrained, and structured settings, with works like Pure Exploration Multi-Armed[16] and Combinatorial Pure Exploration[31] establishing early frameworks. Episodic and Full MDP Pure Exploration extends these ideas to sequential decision problems, where agents must explore state-action spaces under episodic constraints, as exemplified by Episodic Fixed-Horizon MDP[24]. Meta-Learning and In-Context Exploration Strategies represent a newer direction, leveraging prior task experience to accelerate exploration, with In-Context Pure Exploration[10] and Meta-Learning Exploration[18] demonstrating how learned policies can adapt quickly. Theoretical Foundations and Lower Bounds provide rigorous characterizations of sample complexity, while Applications and Domain-Specific Exploration translate these methods to real-world problems ranging from hyperparameter tuning to resource allocation. Several active lines of work reveal key trade-offs between generality and efficiency. Constrained and budgeted settings, explored in Constrained Budget Bandits[3] and Knapsack RL[2], introduce resource limitations beyond sample counts, adding practical realism but complicating algorithm design. Instance-dependent approaches seek to exploit problem structure for tighter guarantees, contrasting with worst-case analyses. Within this landscape, Instance Dependent Budget Exploration[0] sits naturally in the Episodic Fixed-Horizon MDP branch alongside Episodic Fixed-Horizon MDP[24], focusing on how instance-specific properties can be leveraged to improve fixed-budget exploration in episodic settings. While Episodic Fixed-Horizon MDP[24] provides foundational algorithms for this problem class, Instance Dependent Budget Exploration[0] emphasizes adaptive strategies that tailor exploration to the particular MDP instance at hand, bridging classical episodic methods with the growing interest in instance-optimality seen in works like Instance Optimal Linear[41].

Claimed Contributions

BREA algorithm with instance-dependent ε-uniform guarantee

The authors introduce BREA, a fixed-budget pure exploration algorithm for episodic MDPs that provides instance-dependent guarantees. The algorithm characterizes budget requirements in terms of problem-specific exploration hardness and ensures ε-correctness simultaneously for all ε above a budget-dependent threshold, without requiring ε or δ as input.

3 retrieved papers
ε-uniform guarantee for multiple bandit problem

The authors provide the first ε-uniform guarantee for the Successive Accepts and Rejects (SAR) algorithm applied to the multiple bandit problem, where multiple multi-armed bandit instances must be solved simultaneously. This result may be of independent interest beyond the main MDP setting.

3 retrieved papers
Fixed-budget reward-free exploration tools

The authors develop new algorithmic and analytical tools for reward-free exploration under the fixed-budget setting by adapting the Learn2Explore (L2E) algorithm. They prove an ε-uniform guarantee for their fixed-budget reward-free algorithms, which they believe will be useful for future work.

3 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

BREA algorithm with instance-dependent ε-uniform guarantee

The authors introduce BREA, a fixed-budget pure exploration algorithm for episodic MDPs that provides instance-dependent guarantees. The algorithm characterizes budget requirements in terms of problem-specific exploration hardness and ensures ε-correctness simultaneously for all ε above a budget-dependent threshold, without requiring ε or δ as input.

Contribution

ε-uniform guarantee for multiple bandit problem

The authors provide the first ε-uniform guarantee for the Successive Accepts and Rejects (SAR) algorithm applied to the multiple bandit problem, where multiple multi-armed bandit instances must be solved simultaneously. This result may be of independent interest beyond the main MDP setting.

Contribution

Fixed-budget reward-free exploration tools

The authors develop new algorithmic and analytical tools for reward-free exploration under the fixed-budget setting by adapting the Learn2Explore (L2E) algorithm. They prove an ε-uniform guarantee for their fixed-budget reward-free algorithms, which they believe will be useful for future work.

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