The paper studies how a posterior approximation must preserve a specific downstream decision problem. It introduces a regret geometry defined by the target posterior and loss, and uses the forward‑Kullback‑Leibler divergence from a baseline approximation to quantify the information needed for action changes. By analyzing the generalized eigenproblem of the regret Hessian and the baseline information metric, the authors derive a tolerance‑dependent effective dimension and show how restricted approximation families can either miss crucial decision directions or incur excess Fisher information costs.
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:2606. 04845v1 Announce Type: cross Abstract: Sequential decision-making problems are often modelled as a Markov decision process (MDP).
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: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.
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:2610. 12153v1 Announce Type: new Abstract: We study episodic constrained Markov decision processes with adversarial losses under stochastic hard constraints.
arXiv:2608. 01130v1 Announce Type: new Abstract: A broad range of models face the mismatch where they are updated through trajectory losses but are evaluated by downstream task reward.
arXiv:2603. 02491v3 Announce Type: replace-cross Abstract: As artificial agents become increasingly capable, what internal structure is necessary for an agent to act competently under uncertainty?
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 how the Bayesian Learning Rule (BLR), traditionally tied to Kullback‑Leibler divergence, can be extended to other geometries. It demonstrates that additive BLR updates are possible using mixed‑space Bregman or Fenchel‑Young discrepancies, leading to generalized maximum‑entropy families and new canonical gradient updates. For example, applying the Tsallis negentropy with quadratic statistics yields bounded‑support, heavy‑tailed q‑Gaussian posteriors and a simple Newton‑like implementation, with experiments on CIFAR‑100 showing controllable support and tail behavior and competitive performance.
arXiv:2607. 08971v1 Announce Type: new Abstract: The stochastic linear bandit, where actions are represented as vectors and rewards are linear, is a central paradigm for sequential decision making.
arXiv:2610.20187v1 Announce Type: new Abstract: Tracking changing comparators is a central problem in online learning. For exp-concave losses, previous work established the $T^{1/3}P_T^{2/3}$ depende...