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Efficient exact algorithms for Discrete Optimization (DO) rely heavily on strong primal and dual bounds. Relaxed Decision Diagrams (DDs) provide a versatile mechanism for deriving such dual bounds by compactly over-approximating the…
We consider a settings of hierarchical reinforcement learning, in which the reward is a sum of components. For each component we are given a policy that maximizes it and our goal is to assemble a policy from the individual policies that…
Heuristic algorithms such as simulated annealing, Concorde, and METIS are effective and widely used approaches to find solutions to combinatorial optimization problems. However, they are limited by the high sample complexity required to…
Cylindrical algebraic decomposition(CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. When using CAD, there is often a choice for the ordering placed on the variables.…
We propose a new methodology for parameterized constrained robust optimization, an important class of optimization problems under uncertainty, based on learning with a self-supervised penalty-based loss function. Whereas supervised learning…
Efficient sampling from constraint manifolds, and thereby generating a diverse set of solutions for feasibility problems, is a fundamental challenge. We consider the case where a problem is factored, that is, the underlying nonlinear…
Many sequential decision-making problems can be formulated as shortest-path problems, where the objective is to reach a goal state from a given starting state. Heuristic search is a standard approach for solving such problems, relying on a…
Autonomous learning of robotic skills can allow general-purpose robots to learn wide behavioral repertoires without requiring extensive manual engineering. However, robotic skill learning methods typically make one of several trade-offs to…
Policy gradient (PG) is widely used in reinforcement learning due to its scalability and good performance. In recent years, several variance-reduced PG methods have been proposed with a theoretical guarantee of converging to an approximate…
This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…
The considered problem is how to optimally allocate a set of jobs to technicians of different skills such that the number of technicians of each skill does not exceed the number of persons with that skill designation. The key motivation is…
Job-shop scheduling problem (JSP) is a mathematical optimization problem widely used in industries like manufacturing, and flexible JSP (FJSP) is also a common variant. Since they are NP-hard, it is intractable to find the optimal solution…
Combinatorial problems stated as Constraint Satisfaction Problems (CSP) are examined. It is shown by example that any algorithm designed for the original CSP, and involving the AllDifferent constraint, has at least the same level of…
Recent studies in using deep reinforcement learning (DRL) to solve Job-shop scheduling problems (JSSP) focus on construction heuristics. However, their performance is still far from optimality, mainly because the underlying graph…
Safe reinforcement learning (RL) aims to learn policies that satisfy certain constraints before deploying them to safety-critical applications. Previous primal-dual style approaches suffer from instability issues and lack optimality…
We consider the problem of reinforcement learning when provided with (1) a baseline control policy and (2) a set of constraints that the learner must satisfy. The baseline policy can arise from demonstration data or a teacher agent and may…
The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of…
We propose a formulation of the stochastic cutting stock problem as a discounted infinite-horizon Markov decision process. At each decision epoch, given current inventory of items, an agent chooses in which patterns to cut objects in stock…
The performance of the code a compiler generates depends on the order in which it applies the optimization passes. Choosing a good order--often referred to as the phase-ordering problem, is an NP-hard problem. As a result, existing…
In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…