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ARXIV:2603.23926 · REINFORCEMENT LEARNING THEORY · SUBMITTED 02 APR · 02:30 UTC · FRESHNESS STALE
ARXIV:2603.23926REINFORCEMENT LEARNING THEORYSUBMITTED 02 APR · 02:30 UTCFRESHNESS STALEGuy Zamir · Matthew Zurek · Yudong Chen · arXiv
Develops theoretical optimal regret bounds for infinite-horizon reinforcement learning problems.
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Pain Develops theoretical optimal regret bounds for infinite-horizon reinforcement learning problems.
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Develops theoretical optimal regret bounds for infinite-horizon reinforcement learning problems. In this work, we address these shortcomings for two infinite-horizon objectives: the classical average-reward regret and the $γ$-regret.
Online reinforcement learning in infinite-horizon Markov decision processes (MDPs) remains less theoretically and algorithmically developed than its episodic counterpart, with many algorithms suffering from high ``burn-in'' costs and failing to adapt to benign instance-specific…
ScienceToStartup currently rates this 2.0/10 on the public viability pass. We develop a single tractable UCB-style algorithm applicable to both settings, which achieves the first optimal variance-dependent regret guarantees.
Reinforcement Learning Theory moved forward this cycle; last verified April 2026. Public score 2.0/10.
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Develops theoretical optimal regret bounds for infinite-horizon reinforcement learning problems.
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10.48550/arXiv.2603.23926Develops theoretical optimal regret bounds for infinite-horizon reinforcement learning problems.
Abstract
Online reinforcement learning in infinite-horizon Markov decision processes (MDPs) remains less theoretically and algorithmically developed than its episodic counterpart, with many algorithms suffering from high ``burn-in'' costs and failing to adapt to benign instance-specific complexity. In this work, we address these shortcomings for two infinite-horizon objectives: the classical average-reward regret and the $γ$-regret. We develop a single tractable UCB-style algorithm applicable to both settings, which achieves the first optimal variance-dependent regret guarantees. Our regret bounds in both settings take the form $\tilde{O}( \sqrt{SA\,\text{Var}} + \text{lower-order terms})$, where $S,A$ are the state and action space sizes, and $\text{Var}$ captures cumulative transition variance. This implies minimax-optimal average-reward and $γ$-regret bounds in the worst case but also adapts to easier problem instances, for example yielding nearly constant regret in deterministic MDPs. Furthermore, our algorithm enjoys significantly improved lower-order terms for the average-reward setting. With prior knowledge of the optimal bias span $\Vert h^\star\Vert_\text{sp}$, our algorithm obtains lower-order terms scaling as $\Vert h^\star\Vert_\text{sp} S^2 A$, which we prove is optimal in both $\Vert h^\star\Vert_\text{sp}$ and $A$. Without prior knowledge, we prove that no algorithm can have lower-order terms smaller than $\Vert h^\star \Vert_\text{sp}^2 S A$, and we provide a prior-free algorithm whose lower-order terms scale as $\Vert h^\star\Vert_\text{sp}^2 S^3 A$, nearly matching this lower bound. Taken together, these results completely characterize the optimal dependence on $\Vert h^\star\Vert_\text{sp}$ in both leading and lower-order terms, and reveal a fundamental gap in what is achievable with and without prior knowledge.
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PROBLEM
Develops theoretical optimal regret bounds for infinite-horizon reinforcement learning problems. In this work, we address these shortcomings for two infinite-horizon objectives: the classical average-reward regret and the $γ$-regret.
METHOD
Online reinforcement learning in infinite-horizon Markov decision processes (MDPs) remains less theoretically and algorithmically developed than its episodic counterpart, with many algorithms suffering from high ``burn-in'' costs and failing to adapt to benign instance-specific...
RESULT
ScienceToStartup currently rates this 2.0/10 on the public viability pass. We develop a single tractable UCB-style algorithm applicable to both settings, which achieves the first optimal variance-dependent regret guarantees.
WHY NOW
Reinforcement Learning Theory moved forward this cycle; last verified April 2026. Public score 2.0/10.
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Develops theoretical optimal regret bounds for infinite-horizon reinforcement learning problems. In this work, we address these shortcomings for two infinite-horizon objectives: the classical average-reward regret and the $γ$-regret.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
Online reinforcement learning in infinite-horizon Markov decision processes (MDPs) remains less theoretically and algorithmically developed than its episodic counterpart, with many algorithms suffering from high ``burn-in'' costs and failing to adapt to benign instance-specific complexity. In this work, we address these shortcomings for two infinite-horizon objectives: the classical average-reward regret and the $γ$-regret.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
ScienceToStartup currently rates this 2.0/10 on the public viability pass. We develop a single tractable UCB-style algorithm applicable to both settings, which achieves the first optimal variance-dependent regret guarantees.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
Reinforcement Learning Theory moved forward this cycle; last verified April 2026. Public score 2.0/10.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
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Develops theoretical optimal regret bounds for infinite-horizon reinforcement learning problems.
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