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.
arXiv:2511.20413v2 Announce Type: replace-cross Abstract: \emph{Decision-focused learning} (DFL) trains predictive models to optimize downstream decisions rather than prediction accuracy alone. While...
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:2511. 16340v2 Announce Type: replace Abstract: Efficient Gaussian process (GP) inference is critical for sequential decision-making tasks such as active learning, online prediction, and Bayesian optimization.
arXiv:2601. 07094v2 Announce Type: replace-cross Abstract: Bayesian optimization (BO) iteratively fits a Gaussian process (GP) surrogate to accumulated evaluations and selects new queries via an acquisition function.
arXiv:2507.06529v2 Announce Type: replace Abstract: Bayesian optimization (BO) is a powerful paradigm for optimizing expensive black-box functions. Traditional BO methods typically rely on separate h...
This paper tackles Bayesian optimization using Gaussian processes, focusing on minimizing regret when the objective function is drawn from a known GP. For a Matérn kernel with sufficient smoothness, the authors prove that the GP-UCB algorithm achieves a cumulative regret of “~O(√T) with high probability. They also establish an “O(√T ln²T)" regret bound for the squared exponential kernel, bridging the gap between previous upper bounds and Scarlett’s 2018 results. The analysis hinges on capturing the concentration of the input sequence generated by GP-UCB to refine the GP’s information‑gain estimates.
arXiv:2603. 08287v2 Announce Type: replace-cross Abstract: We analyze the Bayesian regret of the Gaussian process posterior sampling reinforcement learning (GP-PSRL) algorithm.
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 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: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.
arXiv:2606. 18778v1 Announce Type: new Abstract: Online learning in non-stationary streams is often formulated as tracking a point estimate, but many applications require predicting the full data-generating distribution.
arXiv:2602.08372v2 Announce Type: replace Abstract: We study dynamic regret minimization in non-stationary online learning, with a primary focus on follow-the-regularized-leader (FTRL) methods. FTRL...