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We investigate the problem of best policy identification in discounted linear Markov Decision Processes in the fixed confidence setting under a generative model. We first derive an instance-specific lower bound on the expected number of…
We address the design and synthesis of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random…
This research considers the ranking and selection with input uncertainty. The objective is to maximize the posterior probability of correctly selecting the best alternative under a fixed simulation budget, where each alternative is measured…
Automatic numerical algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. The computational cost is often determined \emph{adaptively} by the algorithm based…
We develop a method for policy architecture search and adaptation via gradient-free optimization which can learn to perform autonomous driving tasks. By learning from both demonstration and environmental reward we develop a model that can…
Dynamic pricing is crucial in sectors like e-commerce and transportation, balancing exploration of demand patterns and exploitation of pricing strategies. Existing methods often require precise knowledge of the demand function, e.g., the…
Motion planning under differential constraints is a classic problem in robotics. To date, the state of the art is represented by sampling-based techniques, with the Rapidly-exploring Random Tree algorithm as a leading example. Yet, the…
We study the policy evaluation problem in an online multi-reward multi-policy discounted setting, where multiple reward functions must be evaluated simultaneously for different policies. We adopt an $(\epsilon,\delta)$-PAC perspective to…
We formulate selecting the best optimizing system (SBOS) problems and provide solutions for those problems. In an SBOS problem, a finite number of systems are contenders. Inside each system, a continuous decision variable affects the…
This paper bridges some of the gap between optimal planning and reinforcement learning (RL), both of which share roots in dynamic programming applied to sequential decision making or optimal control. Whereas planning typically favors…
We consider a context-dependent ranking and selection problem. The best design is not universal but depends on the contexts. Under a Bayesian framework, we develop a dynamic sampling scheme for context-dependent optimization (DSCO) to…
We study two-stage distributionally robust optimization (DRO) problems with decision-dependent information discovery (DDID) wherein (a portion of) the uncertain parameters are revealed only if an (often costly) investment is made in the…
We study reinforcement learning for controlled diffusion processes with unbounded continuous state spaces, bounded continuous actions, and polynomially growing rewards: settings that arise naturally in finance, economics, and operations…
In reinforcement learning, an agent attempts to learn high-performing behaviors through interacting with the environment, such behaviors are often quantified in the form of a reward function. However some aspects of behavior-such as ones…
We study the problem of pure exploration in matching markets under uncertain preferences, where the goal is to identify a stable matching with confidence parameter $\delta$ and minimal sample complexity. Agents learn preferences via…
In this work, we provide theoretical guarantees for reward decomposition in deterministic MDPs. Reward decomposition is a special case of Hierarchical Reinforcement Learning, that allows one to learn many policies in parallel and combine…
We consider deterministic infinite horizon optimal control problems with nonnegative stage costs. We draw inspiration from learning model predictive control scheme designed for continuous dynamics and iterative tasks, and propose a rollout…
Diffusion models excel at modeling complex and multimodal trajectory distributions for decision-making and control. Reward-gradient guided denoising has been recently proposed to generate trajectories that maximize both a differentiable…
Dynamic optimization problems (DOPs) are challenging due to their changing conditions. This requires algorithms to be highly adaptable and efficient in terms of finding rapidly new optimal solutions under changing conditions. Traditional…
In this paper we study the non-stationary stochastic optimization question with bandit feedback and dynamic regret measures. The seminal work of Besbes et al. (2015) shows that, when aggregated function changes is known a priori, a simple…