Related papers: UCB for Large-Scale Pure Exploration: Beyond Sub-G…
The regret lower bound of Lai and Robbins (1985), the gold standard for checking optimality of bandit algorithms, considers arm size fixed as sample size goes to infinity. We show that when arm size increases polynomially with sample size,…
Maximizing high-dimensional, non-convex functions through noisy observations is a notoriously hard problem, but one that arises in many applications. In this paper, we tackle this challenge by modeling the unknown function as a sample from…
We analyze a tree search problem with an underlying Markov decision process, in which the goal is to identify the best action at the root that achieves the highest cumulative reward. We present a new tree policy that optimally allocates a…
Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…
We introduce in this paper a new algorithm for Multi-Armed Bandit (MAB) problems. A machine learning paradigm popular within Cognitive Network related topics (e.g., Spectrum Sensing and Allocation). We focus on the case where the rewards…
We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…
The recent rising popularity of ultra-fast delivery services on retail platforms fuels the increasing use of urban warehouses, whose proximity to customers makes fast deliveries viable. The space limit in urban warehouses poses a problem…
We consider the problem of quantifying the quality of a model selection problem for a graphical model. We discuss this by formulating the problem as a detection problem. Model selection problems usually minimize a distance between the…
Bayesian optimization is a framework for global search via maximum a posteriori updates rather than simulated annealing, and has gained prominence for decision-making under uncertainty. In this work, we cast Bayesian optimization as a…
Despite being successful in board games and reinforcement learning (RL), Monte Carlo Tree Search (MCTS) combined with Multi Armed Bandits (MABs) has seen limited success in domain-independent classical planning until recently. Previous work…
Safety-critical control systems, such as spacecraft performing proximity operations, must provide formal safety guarantees despite stochastic uncertainties from state estimation and unmodeled dynamics. Although Control Barrier Functions…
The combinatorial pure exploration of causal bandits is the following online learning task: given a causal graph with unknown causal inference distributions, in each round we choose a subset of variables to intervene or do no intervention,…
In this paper, we consider the Gaussian process (GP) bandit optimization problem in a non-stationary environment. To capture external changes, the black-box function is allowed to be time-varying within a reproducing kernel Hilbert space…
This paper presents a new multi-query motion planning algorithm for linear Gaussian systems with the goal of reaching a Euclidean ball with high probability. We develop a new formulation for ball-shaped ambiguity sets of Gaussian…
This paper investigates the problem of efficient constrained global optimization of hybrid models that are a composition of a known white-box function and an expensive multi-output black-box function subject to noisy observations, which…
Gaussian Process (GP) models have also become extremely useful for optimization under uncertainty algorithms, especially where the objective functions are costly to compute. Yet, the more classical methods usually adopt strategies that, in…
We study fine-grained gap-dependent regret bounds for model-free reinforcement learning in episodic tabular Markov Decision Processes. Existing model-free algorithms achieve minimax worst-case regret, but their gap-dependent bounds remain…
Bayesian optimization has been successfully applied to optimize black-box functions where the number of evaluations is severely limited. However, in many real-world applications, it is hard or impossible to know in advance which designs are…
Many of the causal discovery methods rely on the faithfulness assumption to guarantee asymptotic correctness. However, the assumption can be approximately violated in many ways, leading to sub-optimal solutions. Although there is a line of…
The multi-armed bandit (MAB) problem is a foundational framework in sequential decision-making under uncertainty, extensively studied for its applications in areas such as clinical trials, online advertising, and resource allocation.…