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We present two elegant solutions for modeling continuous-time dynamics, in a novel model-based reinforcement learning (RL) framework for semi-Markov decision processes (SMDPs), using neural ordinary differential equations (ODEs). Our models…

We consider solving high-order semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the SDP alone, we propose a new…

We consider online reinforcement learning in episodic Markov decision process (MDP) with unknown transition function and stochastic rewards drawn from some fixed but unknown distribution. The learner aims to learn the optimal policy and…

A recent goal in the Reinforcement Learning (RL) framework is to choose a sequence of actions or a policy to maximize the reward collected or minimize the regret incurred in a finite time horizon. For several RL problems in operation…

Reinforcement learning (RL) is a fundamental framework for sequential decision-making, in which an agent learns an optimal policy through interactions with an unknown environment. In settings with function approximation, many existing RL…

Several real-world scenarios, such as remote control and sensing, are comprised of action and observation delays. The presence of delays degrades the performance of reinforcement learning (RL) algorithms, often to such an extent that…

A Budgeted Markov Decision Process (BMDP) is an extension of a Markov Decision Process to critical applications requiring safety constraints. It relies on a notion of risk implemented in the shape of a cost signal constrained to lie below…

The continuous dynamical system approach to deep learning is explored in order to devise alternative frameworks for training algorithms. Training is recast as a control problem and this allows us to formulate necessary optimality conditions…

Efficient representations and solutions for large decision problems with continuous and discrete variables are among the most important challenges faced by the designers of automated decision support systems. In this paper, we describe a…

Continuous state spaces and stochastic, switching dynamics characterize a number of rich, realworld domains, such as robot navigation across varying terrain. We describe a reinforcementlearning algorithm for learning in these domains and…

Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However,…

Bayesian approaches developed to solve the optimal design of sequential experiments are mathematically elegant but computationally challenging. Recently, techniques using amortization have been proposed to make these Bayesian approaches…

Sampling efficiency is critical for deploying visuomotor learning in real-world robotic manipulation. While task symmetry has emerged as a promising inductive bias to improve efficiency, most prior work is limited to isometric symmetries --…

We study reinforcement learning with function approximation for large-scale Partially Observable Markov Decision Processes (POMDPs) where the state space and observation space are large or even continuous. Particularly, we consider Hilbert…

Reinforcement Learning (RL) has demonstrated strong potential for industrial process control, yet policies trained in simulation often suffer from a significant sim-to-real gap when deployed on physical hardware. This work systematically…

Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…

Domain-Independent Dynamic Programming (DIDP) is a state-space search paradigm based on dynamic programming for combinatorial optimization. In its current implementation, DIDP guides the search using user-defined dual bounds. Reinforcement…

Partially observable Markov decision processes (POMDPs) are a natural model for planning problems where effects of actions are nondeterministic and the state of the world is not completely observable. It is difficult to solve POMDPs…

The Robust Markov Decision Process (RMDP) framework focuses on designing control policies that are robust against the parameter uncertainties due to the mismatches between the simulator model and real-world settings. An RMDP problem is…

Optimal policies in Markov decision processes (MDPs) are very sensitive to model misspecification. This raises serious concerns about deploying them in high-stake domains. Robust MDPs (RMDP) provide a promising framework to mitigate…