arXiv:2606. 11171v2 Announce Type: replace Abstract: We develop indexed Bellman information complexity, a representation-level theory of interactive decision making centered on information indices and reference histories.
arXiv:2602. 09456v2 Announce Type: replace Abstract: We propose an algorithmic framework, Offline Estimation to Decisions (OE2D), that efficiently reduces contextual bandit learning with general reward function approximation to offline regression.
arXiv:2607. 08979v1 Announce Type: new Abstract: We study the active learning problem of fixed-confidence top-$k$ identification from noisy pairwise comparisons.
arXiv:2608. 18061v1 Announce Type: new Abstract: We give a two-player zero-sum repeated game between a learner and nature whose value identity generates Bayesian updating and an exact accounting of exponential-weights regret at once, and supplies the comparator-class variational form that a wide class of concentration phenomena share.
arXiv:2605. 09454v2 Announce Type: replace-cross Abstract: We study the $\textit{single-index bandit}$ problem, where rewards depend on an unknown one-dimensional projection of high-dimensional contexts through an unknown reward function.
arXiv:2608. 10650v1 Announce Type: new Abstract: Reducing the number of focal elements of a mass function is classically driven by an intrinsic distance, such as Jaccard or Jousselme, that keeps the approximation close to the original as a body of evidence.
arXiv:2606. 28616v1 Announce Type: new Abstract: In stochastic linear bandits, the canonical Upper Confidence Bound (UCB) algorithm admits a simple frequentist regret analysis but can be computationally demanding, while Thompson Sampling (TS) is computationally attractive yet typically harder to analyze due to its non-optimistic nature.
arXiv:2606. 08028v1 Announce Type: new Abstract: We study high-probability regret bounds for online convex optimization (OCO) with strongly convex losses and establish three results that resolve open questions at the intersection of noise adaptivity, feedback structure, and constraint satisfaction.
Minimax risk and regret are expectation-based criteria and do not capture rare but consequential failures. To address this concern, we develop a $δ$-explicit minimax-quantile theory for interactive statistical decision making (ISDM).
arXiv:2608. 01069v1 Announce Type: new Abstract: Bandit algorithms generate data for downstream inference, but adaptive sampling biases post-bandit sample means.
arXiv:2606. 14690v1 Announce Type: new Abstract: We study a \emph{max-risk} objective for active learning in a multi-group mean estimation $d$-armed bandits: a learner adaptively allocates a budget of $T$ samples across $d$ groups to minimize the worst-case uncertainty index $\max_{k\in[d]}\sigma_k^2/n_k$, where $\sigma_k$ is the standard deviation of the distribution of arm $d$, and $n_k$ is the number of times arm $d$ is sampled.
arXiv:2606. 11171v1 Announce Type: new Abstract: Gaussian-process upper confidence bound (GP-UCB) and decision-estimation-coefficient (DEC) methods may appear, at first sight, to belong to different theories.
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.