A new arXiv paper studies stochastic linear contextual bandits where the set of available actions can vary arbitrarily, depending on both the unknown parameter and past interactions. The authors prove matching upper and lower bounds on regret that agree up to logarithmic factors, characterizing the problem's minimax rate.
This paper studies adversarial multi-armed bandit problems in which the benchmark arm sequence may change up to S times over the course of play, a setting known as switching regret. It reviews and develops regret guarantees of order the square root of (S+1)KT, which prior work showed is achievable when S is known in advance. The work aims to pin down the optimal achievable rate under an oblivious adversary.
A new arXiv paper studies decentralized online optimization where the decision variables live on Hadamard manifolds, a setting with negative curvature. The authors derive regret guarantees that do not depend on the manifold's curvature, avoiding the finite lower bound on sectional curvature required by earlier analyses built on geodesic convexity. The results apply to distributed multi-agent settings where agents coordinate over a network while optimizing online.
A new arXiv paper examines constrained online convex optimization where both constraint values and gradients are observed with noise. The authors introduce an algorithm called LEDGER, which they show achieves O(√T) expected regret and constraint violation under standard feasibility assumptions. The work targets settings with adversarial constraints and conditionally unbiased, finite-variance observations.
A new arXiv paper examines how few models are needed in ensemble sampling, a randomized-exploration method for sequential decision problems, while still preserving theoretical regret bounds. Prior results relied on ensembles larger than practical implementations typically use, leaving the minimum viable size unclear. The work analyzes this setting for linear models.
A new arXiv paper presents a deterministic algorithm for online inverse linear optimization that attains O(d) regret, a bound that holds uniformly across the time horizon. Each round requires O(d^2) computation time. The result matches a recent bound by Dewasurendra and addresses an open question raised by Gollapudi and colleagues.
A newly posted arXiv paper investigates how online learning methods such as gradient descent, mirror descent, and follow-the-regularized-leader behave when measured against more demanding, action-dependent benchmarks rather than fixed comparison points. Moving past the standard external regret framing, the authors pursue a geometric account of these deviations and derive closed-form expressions for the resulting regret bounds.