We develop a new class of approximate linear programs (ALPs) that project the high-dimensional value function of dynamic programs onto a class of basis functions, each defined as a network that represents aggregrations over the state space. The resulting ALP is a minimum-cost flow problem over an extended variable space that synchronizes flows across multiple … Read more
It is shown how to use the performance and data profile benchmarking tools to improve algorithms’ performance. An illustration for the BFO derivative-free optimizer suggests that the obtained gains are potentially significant. Citation ACM Transactions on Mathematical Software, 45:2 (2019), Article 20. Article Download View A note on using performance and data profiles for training … Read more
We consider an n-player non-cooperative game with random payoffs and continuous strategy set for each player. The random payoffs of each player are defined using a finite dimensional random vector. We formulate this problem as a chance-constrained game by defining the payoff function of each player using a chance constraint. We first consider the case … Read more
In the analysis of complex stochastic dynamic programs, we often seek strong theoretical guarantees on the suboptimality of heuristic policies. One technique for obtaining performance bounds is perfect information analysis: this approach provides bounds on the performance of an optimal policy by considering a decision maker who has access to the outcomes of all future … Read more
In the meta-modeling approach one builds a numerically tractable dynamic optimization or game model in which the parameters are identified through statistical emulation of a detailed large scale numerical simulation model. In this paper we show how this approach can be used to assess the economic impacts of possible climate policies compatible with the Paris … Read more
We describe a nonlinear generalization of dual dynamic programming theory and its application to value function estimation for deterministic control problems over continuous state and action (or input) spaces, in a discrete-time infinite horizon setting. We prove that the result of a one-stage policy evaluation can be used to produce nonlinear lower bounds on the … Read more
In this paper, the aim is to compute Pareto efficient solutions of multi-objective optimization problems involving forbidden regions. More precisely, we assume that the vector-valued objective function is componentwise generalized-convex and acts between a real topological linear pre-image space and a finite-dimensional image space, while the feasible set is given by the whole pre-image space … Read more
We consider the Resource Constrained Shortest Path problem arising as a subproblem in state-of-the-art Branch-Cut-and-Price algorithms for vehicle routing problems. We propose a variant of the bi-directional label correcting algorithm in which the labels are stored and extended according to so-called bucket graph. Such organization of labels helps to decrease significantly the number of dominance … Read more
Consider the problem of approximating the optimal policy of a Markov decision process (MDP) by sampling state transitions. In contrast to existing reinforcement learning methods that are based on successive approximations to the nonlinear Bellman equation, we propose a Primal-Dual π Learning method in light of the linear duality between the value and policy. The … Read more
Multi-stage stochastic optimization is a well-known quantitative tool for decision-making under uncertainty, which applications include financial and investment planning, inventory control, energy production and trading, electricity generation planning, supply chain management and similar fields. Theoretical solution of multi-stage stochastic programs can be found explicitly only in very exceptional cases due to the complexity of the … Read more