aiqbench analysis
This article's primary subject is a theoretical machine learning result: a bandit algorithm (EL-F, an empirical-likelihood extension of g-Forcing) with regret guarantees under unknown reward scales. It fits squarely within Machine Learning rather than the applied or policy categories. For readers, the practical takeaway is that the work offers finite-run tail bounds and expected-regret guarantees for a scale-free exploration policy, which addresses a real gap between asymptotic and finite-sample analysis, though results are so far limited to specific instance classes and experiments.
Reliable Scale-Free Bandits via Empirical Likelihood
arXiv:2610.18055v1 Announce Type: cross Abstract: We study stochastic bandits without knowledge of reward scales or tail parameters. Almost-sure regret guarantees describe eventual learning but do not quantify expected performance or the risk of large regret in a finite run. We introduce $\texttt{EL-F}$, an anytime empirical-likelihood (EL) extension of the $g$-Forcing policy of Cowan and Katehakis (2020), and characterize its performance at three levels. First, for integrable rewards and non-decreasing, diverging exploration schedules $g$ with vanishing increments, $\texttt{EL-F}$ preserves the $g$-Forcing asymptotics for pseudo-regret $R(T)$: $R(T)/g(T)\to\sum_{i:\Delta_i>0}\Delta_i$ almost surely as $T\to\infty$, where $\Delta_i$ is the suboptimality gap of arm $i$. Second, on every sub-exponential instance, for non-decreasing $g(t)=\omega(\log t)$ satisfying a mild feasibility condition, expected pseudo-regret is at most $g(T)\sum_{i:\Delta_i>0}\Delta_i+C_{\underline{P}}$, where $C_{\underline{P}}$ is an instance-dependent constant independent of $T$. Moreover, we also establish finite-time tail bounds with super-polynomial decay in regret beyond the forced-exploration budget. For slowly varying $g$, we determine the exact exponent of linear regret deviations on two-armed Gaussian instances with common variance and establish a matching lower bound among policies satisfying the same expected-regret budget on every such Gaussian instance. These quantitative guarantees also cover the greedy variant obtained at zero EL radius. A fixed positive radius introduces local optimism while preserving the leading asymptotic regret. We establish coupled pathwise dominance over the greedy variant in two-armed bandits with a deterministic suboptimal arm. Experiments demonstrate reductions in prolonged suboptimal allocation compared with $g$-Forcing on challenging instances.
Abstract:We study stochastic bandits without knowledge of reward scales or tail parameters. Almost-sure regret guarantees describe eventual learning but do not quantify expected performance or the risk of large regret in a finite run. We introduce $\texttt{EL-F}$, an anytime empirical-likelihood (EL) extension of the $g$-Forcing policy of Cowan and Katehakis (2020), and characterize its performance at three levels. First, for integrable rewards and non-decreasing, diverging exploration schedules $g$ with vanishing increments, $\texttt{EL-F}$ preserves the $g$-Forcing asymptotics for pseudo-regret $R(T)$: $R(T)/g(T)\to\sum_{i:\Delta_i>0}\Delta_i$ almost surely as $T\to\infty$, where $\Delta_i$ is the suboptimality gap of arm $i$. Second, on every sub-exponential instance, for non-decreasing $g(t)=\omega(\log t)$ satisfying a mild feasibility condition, expected pseudo-regret is at most $g(T)\sum_{i:\Delta_i>0}\Delta_i+C_{\underline{P}}$, where $C_{\underline{P}}$ is an instance-dependent constant independent of $T$. Moreover, we also establish finite-time tail bounds with super-polynomial decay in regret beyond the forced-exploration budget. For slowly varying $g$, we determine the exact exponent of linear regret deviations on two-armed Gaussian instances with common variance and establish a matching lower bound among policies satisfying the same expected-regret budget on every such Gaussian instance. These quantitative guarantees also cover the greedy variant obtained at zero EL radius. A fixed positive radius introduces local optimism while preserving the leading asymptotic regret. We establish coupled pathwise dominance over the greedy variant in two-armed bandits with a deterministic suboptimal arm. Experiments demonstrate reductions in prolonged suboptimal allocation compared with $g$-Forcing on challenging instances.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2610.18055 [stat.ML]
(or arXiv:2610.18055v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.18055 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 329 words
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