The paper introduces the tilted sampling problem, where an online learner aims to sample from a Gibbs distribution defined by an unknown reward function. It defines sampling regret as the temperature‑normalized cumulative KL divergence between the learner’s distribution and the target Gibbs distribution, linking it to entropy‑regularized reward maximization. The authors develop sampling analogues of UCB and Thompson sampling, proving that sampling regret can achieve logarithmic growth in time, unlike standard regret which scales as ×O(√T).
arXiv:2605. 20854v2 Announce Type: replace Abstract: We study a stochastic bandit algorithm motivated by retry-aware objectives that value the best outcome among multiple attempts, such as pass@$k$ and max@$k$.
arXiv:2405.08253v4 Announce Type: replace-cross Abstract: This paper develops a framework for learning in discounted infinite-horizon Markov decision processes (MDPs) with Borel state and action spac...
The paper presents the first high‑probability regret bounds for both cumulative and current‑step variants of Feel‑Good Thompson Sampling (FGTS) in contextual bandits with general realizable function approximation. The bounds rely on decoupling coefficients and prior mass near the true reward function, and in the linear setting they achieve ≠d√T log(2T)+√T log(1/δ) regret with probability at least 1‑δ. This matches the dimension and horizon dependence of upper‑confidence‑bound algorithms up to logarithmic factors, while the high‑probability cost adds only linear dependence on log(1/δ).
arXiv:2607. 28408v1 Announce Type: new Abstract: This thesis studies policy learning in interactive systems where an agent observes a context, selects an action from a very large set, and receives partial feedback.
The paper analyzes Bayesian linear bandits with isotropic Gaussian parameters, independent Gaussian arms, and Gaussian reward noise when the time horizon scales with the dimension. It derives explicit limits for the normalized posterior uncertainty and parameter overlaps, yielding exact regret curves for several policies—including Thompson sampling, posterior‑mean greedy selection, and scaled‑covariance variants. The results show that posterior‑mean greedy selection achieves the optimal Bayes regret, while Thompson sampling incurs a strictly larger leading regret whose ratio to greedy lies between one and two, approaching two for long horizons.
arXiv:2609.13564v1 Announce Type: new Abstract: We study KL-regularized contextual bandits under both reward and preference feedback. We show that greedy sampling can achieve logarithmic regret witho...
arXiv:2605.20854v3 Announce Type: replace Abstract: We provide the first regret analysis of ReMax in stochastic multi-armed bandits. Originally introduced for reinforcement learning, ReMax is motivat...
The paper investigates how fast predictive regret guarantees of exact Bayesian online learning can be maintained when using approximate posterior methods. It establishes a general theorem linking the cumulative cost of posterior approximation to the contraction radius of the exact Gibbs posterior and the Wasserstein distance between approximate and exact posteriors. Three concrete online learning scenarios—linear models, infinite‑dimensional exponential families, and Gaussian process regression—illustrate that appropriately accurate approximations (projected Langevin, truncation, and sparse variational posteriors) preserve fast regret bounds while reducing computational demands.
The paper investigates stochastic contextual bandits in an agnostic setting, aiming to compete with the best policy in a given class without assuming realizability or specific loss/reward models. It introduces an algorithm that updates the policy each round by minimizing a pessimistic objective— a clipped inverse‑propensity estimate of the policy value plus a variance penalty— and proves the first fast regret rates relative to the best‑in‑class policy. By exploiting entropy assumptions on the policy class and a H"olderian error‑bound condition, the authors achieve fast best‑in‑class regret rates, including polylogarithmic rates in the parametric case, using a sequential self‑normalized maximal inequality for bounded martingale empirical processes to derive uniform variance‑adaptive confidence bounds and ensure pessimism under adaptive data collection.
The paper investigates preference-based bandits where a learner selects pairs of arms and receives binary preference feedback modeled by Bradley–Terry. It introduces the locally sensitive eluder dimension, a new complexity measure for logistic preference feedback, and proposes the GINOP algorithm that uses log-loss confidence sets to balance optimism and exploration. The authors prove a first-order regret bound showing that learning with preference feedback can be as statistically efficient as learning from direct rewards, and they validate their theory with empirical experiments.
The paper introduces DUCB-OGD, an algorithm that couples a Discounted Upper‑Confidence‑Bound sampler with Online Gradient Descent to address dynamic minimax regret in robust large‑language‑model post‑training. It operates under instantaneous mini‑batch‑only bandit feedback, tracking worst‑source performance without re‑evaluating historical data. Experiments on fine‑tuning, preference optimization, and reinforcement learning demonstrate that DUCB‑OGD improves worst‑group robustness with negligible computational overhead.
arXiv:2603. 08287v2 Announce Type: replace-cross Abstract: We analyze the Bayesian regret of the Gaussian process posterior sampling reinforcement learning (GP-PSRL) algorithm.