Bayesian online learning promises uncertainty-aware prediction on data streams, but its performance hinges on inferential choices, including learning rates, prior distributions and variational families, which are usually fixed before seeing the stream. We address this by treating Bayesian update rules as experts and aggregating the Bayesian experts according to sequential predictive losses. We prove that the resulting aggregate competes with the best expert in hindsight at an aggregation cost determined by how each expert's per-round performance is evaluated. We instantiate the framework in online conformal inference and Gaussian process regression. The conformal inference application yields a smoothed Bayesian counterpart of adaptive conformal inference with long-run randomized coverage, while the Gaussian process application gives an oracle inequality in cumulative predictive Kullback-Leibler risk and adaptation to unknown Hölder smoothness up to logarithmic factors. Experiments show that the aggregate tracks strong experts without oracle expert selection.
Reinforcement Learning (RL) is a sequential decision-making framework in which an agent learns optimal policies through interaction with an environment by maximizing cumulative rewards. Among RL methods, Bayesian Reinforcement Learning (BRL) addresses common practical challenges…
We introduce Deep Adaptive Bayesian Screening (DABS), a method for performing adaptive factorial screening in high-dimensional discrete design spaces. DABS learns a policy network offline to sequentially select informative experiments, amortizing Bayesian Optimal Experimental Des…
Conservative offline training is widely advocated as a safe foundation for subsequent online adaptation: if a policy stays close to well-supported behaviour, the argument goes, it is less likely to exploit imperfections in a learned reward model. We challenge this intuition empir…
The Continual Learning (CL) literature has long been driven by the goal of mitigating catastrophic forgetting. This objective rests on a pervasive, often unstated assumption: that a lifelong learner should approximate the Joint-Task Learning (JTL) solution and retain all previous…
A central challenge in statistical modeling is identifying the subset of features that belong in the true regression model. The classical best subset selection problem, recently made tractable via mixed-integer optimization (MIO), finds the globally optimal sparse solution. It do…
Policy-based approaches to Bayesian experimental design (BED) allow the learning of deep policy networks that adaptively make intelligent design decisions based on previously collected data. However, the training of such policies is often held back by a fundamental challenge: the…