Reliable Scale-Free Bandits via Empirical Likelihood
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 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, EL−F preserves the g-Forcing asymptotics for pseudo-regret R(T): R(T)/g(T)→∑i:Δi>0Δi almost surely as T→∞, where Δi is the suboptimality gap of arm i. Second, on every sub-exponential instance, for non-decreasing g(t)=ω(log t) satisfying a mild feasibility condition, expected pseudo-regret is at most g(T)∑i:Δi>0Δi+CunderlineP, where CunderlineP 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.
Related
- Bias-Corrected Empirical-Likelihood Inference for Single-Index Expectile Regression Under Missing-at-Random Responses
- Likelihood-Free Inference in High-Dimensional Models
- SLICE: Sequential Likelihood-Free Inference via Conformal E-Values
- Likelihood-free inference with nuisance parameters through normalizing flows
- Likelihood-Free Schrödinger--Föllmer Sampling for Bayesian Inference with Fixed-Proposal Reuse
BibTeX
@misc{gupta2026reliable,
title = {{Reliable Scale-Free Bandits via Empirical Likelihood}},
author = {Pratham Gupta and Alhad Sethi and Shubhada Agrawal},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18055},
eprint = {2610.18055},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18055},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reliable Scale-Free Bandits via Empirical Likelihood
AU - Pratham Gupta
AU - Alhad Sethi
AU - Shubhada Agrawal
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18055
UR - https://arxiv.org/abs/2610.18055
AB - 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 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, EL−F preserves the g-Forcing asymptotics for pseudo-regret R(T): R(T)/g(T)→∑_i:Δ_i>0Δ_i almost surely as T→∞, where Δ_i is the suboptimality gap of arm i. Second, on every sub-exponential instance, for non-decreasing g(t)=ω(log t) satisfying a mild feasibility condition, expected pseudo-regret is at most g(T)∑_i:Δ_i>0Δ_i+C_underlineP, where C_underlineP 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.
ER -