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We consider deterministic Markov decision processes (MDPs) and apply max-plus algebra tools to approximate the value iteration algorithm by a smaller-dimensional iteration based on a representation on dictionaries of value functions. The…

Machine Learning · Computer Science 2019-06-21 Francis Bach

We study computational and statistical aspects of learning Latent Markov Decision Processes (LMDPs). In this model, the learner interacts with an MDP drawn at the beginning of each epoch from an unknown mixture of MDPs. To sidestep known…

Machine Learning · Computer Science 2024-06-13 Fan Chen , Constantinos Daskalakis , Noah Golowich , Alexander Rakhlin

We propose policy gradient algorithms for robust infinite-horizon Markov decision processes (MDPs) with non-rectangular uncertainty sets, thereby addressing an open challenge in the robust MDP literature. Indeed, uncertainty sets that…

Optimization and Control · Mathematics 2025-09-30 Mengmeng Li , Daniel Kuhn , Tobias Sutter

For the problem of task-agnostic reinforcement learning (RL), an agent first collects samples from an unknown environment without the supervision of reward signals, then is revealed with a reward and is asked to compute a corresponding…

Machine Learning · Computer Science 2022-03-16 Jingfeng Wu , Vladimir Braverman , Lin F. Yang

We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a…

Systems and Control · Electrical Eng. & Systems 2022-07-13 Kush Grover , Jan Křetínský , Tobias Meggendorfer , Maximilian Weininger

We study finite horizon optimal switching problems for hidden Markov chain models under partially observable Poisson processes. The controller possesses a finite range of strategies and attempts to track the state of the unobserved state…

Optimization and Control · Mathematics 2008-05-22 Erhan Bayraktar , Mike Ludkovski

Model-based reinforcement learning is a powerful tool, but collecting data to fit an accurate model of the system can be costly. Exploring an unknown environment in a sample-efficient manner is hence of great importance. However, the…

Machine Learning · Computer Science 2023-04-27 Matthieu Blanke , Marc Lelarge

We present Model Predictive Trees (MPT), a receding horizon tree search algorithm that improves its performance by reusing information efficiently. Whereas existing solvers reuse only the highest-quality trajectory from the previous…

Robotics · Computer Science 2024-11-26 John Lathrop , Benjamin Rivi`ere , Jedidiah Alindogan , Soon-Jo Chung

Many processes, such as discrete event systems in engineering or population dynamics in biology, evolve in discrete space and continuous time. We consider the problem of optimal decision making in such discrete state and action space…

Machine Learning · Computer Science 2020-10-27 Bastian Alt , Matthias Schultheis , Heinz Koeppl

Lookahead, also known as non-myopic, Bayesian optimization (BO) aims to find optimal sampling policies through solving a dynamic program (DP) that maximizes a long-term reward over a rolling horizon. Though promising, lookahead BO faces the…

Machine Learning · Computer Science 2022-07-26 Xubo Yue , Raed Al Kontar

There is increasing interest to develop Bayesian inferential algorithms for point process models with intractable likelihoods. A purpose of this paper is to illustrate the utility of using simulation based strategies, including Approximate…

Computation · Statistics 2026-02-02 Chaoyi Lu , Nial Friel

Constrained decision-making is essential for designing safe policies in real-world control systems, yet simulated environments often fail to capture real-world adversities. We consider the problem of learning a policy that will maximize the…

Machine Learning · Computer Science 2026-02-10 Sourav Ganguly , Kishan Panaganti , Arnob Ghosh , Adam Wierman

Practical reinforcement learning problems are often formulated as constrained Markov decision process (CMDP) problems, in which the agent has to maximize the expected return while satisfying a set of prescribed safety constraints. In this…

Machine Learning · Computer Science 2019-09-23 Shin-ichi Maeda , Hayato Watahiki , Shintarou Okada , Masanori Koyama

Learning a near optimal policy in a partially observable system remains an elusive challenge in contemporary reinforcement learning. In this work, we consider episodic reinforcement learning in a reward-mixing Markov decision process (MDP).…

Machine Learning · Computer Science 2022-02-01 Jeongyeol Kwon , Yonathan Efroni , Constantine Caramanis , Shie Mannor

A fundamental question in reinforcement learning is whether model-free algorithms are sample efficient. Recently, Jin et al. \cite{jin2018q} proposed a Q-learning algorithm with UCB exploration policy, and proved it has nearly optimal…

Machine Learning · Computer Science 2019-09-30 Kefan Dong , Yuanhao Wang , Xiaoyu Chen , Liwei Wang

In supervised learning, we fit a single statistical model to a given data set, assuming that the data is associated with a singular task, which yields well-tuned models for specific use, but does not adapt well to new contexts. By contrast,…

Machine Learning · Computer Science 2020-09-11 Bingjia Wang , Alec Koppel , Vikram Krishnamurthy

Constrained Markov Decision Processes (CMDPs) formalize sequential decision-making problems whose objective is to minimize a cost function while satisfying constraints on various cost functions. In this paper, we consider the setting of…

Machine Learning · Computer Science 2020-09-25 Krishna C. Kalagarla , Rahul Jain , Pierluigi Nuzzo

In this paper we consider the problem of how a reinforcement learning agent that is tasked with solving a sequence of reinforcement learning problems (a sequence of Markov decision processes) can use knowledge acquired early in its lifetime…

Machine Learning · Computer Science 2019-02-05 Francisco M. Garcia , Philip S. Thomas

Lazy graph search algorithms are efficient at solving motion planning problems where edge evaluation is the computational bottleneck. These algorithms work by lazily computing the shortest potentially feasible path, evaluating edges along…

Robotics · Computer Science 2019-07-18 Mohak Bhardwaj , Sanjiban Choudhury , Byron Boots , Siddhartha Srinivasa

We optimize finite horizon multi-agent reach-avoid Markov decision process (MDP) via \emph{local feedback policies}. The global feedback policy solution yields global optimality but its communication complexity, memory usage and computation…

Systems and Control · Electrical Eng. & Systems 2026-04-10 Adam Casselman , Abraham P. Vinod , Sarah H. Q. Li