We propose several schemes for upper bounding the optimal value of the constrained most probable explanation (CMPE) problem.

Bandits with knapsacks (BwK) is an influential model of sequential decision-making under uncertainty that incorporates resource consumption constraints. In each round, the decision-maker observes an outcome consisting of a reward and a vector of nonnegative resource consumptions, and the budget of each resource is decremented by its consumption. In this paper we introduce a natural generalization of the stochastic BwK problem that allows non-monotonic resource utilization. In each round, the decision-maker observes an outcome consisting of a reward and a vector of resource drifts that can be positive, negative or zero, and the budget of each resource is incremented by its drift. Our main result is a Markov decision process (MDP) policy that has constant regret against a linear programming (LP) relaxation when the decision-maker knows the true outcome distributions. We build upon this to develop a learning algorithm that has logarithmic regret against the same LP relaxation when the decision-maker does not know the true outcome distributions. We also present a reduction from BwK to our model that shows our regret bound matches existing results.

Smart grid technological advances present a recent class of complex interdisciplinary modeling and increasingly difficult simulation problems to solve using traditional computational methods. To simulate a smart grid requires a systemic approach to integrated modeling of power systems, energy markets, demand-side management, and much other resources and assets that are becoming part of the current paradigm of the power grid. This paper presents a backbone model of a smart grid to test alternative scenarios for the grid. This tool simulates disparate systems to validate assumptions before the human scale model. Thanks to a distributed optimization of subsystems, the production and consumption scheduling is achieved while maintaining flexibility and scalability.

Cutting-planes are one of the most important building blocks for solving large-scale integer programming (IP) problems to (near) optimality.

Column generation and branch-and-price are leading methods for large-scale exact optimization. Column generation iterates between solving a master problem and a pricing problem. The master problem is a linear program, which can be solved using a generic solver. The pricing problem is highly dependent on the application but is usually discrete. Due to the difficulty of discrete optimization, high-performance column generation often relies on a custom pricing algorithm built specifically to exploit the problem's structure. This bespoke nature of the pricing solver prevents the reuse of components for other applications. We show that domain-independent dynamic programming, a software package for modeling and solving arbitrary dynamic programs, can be used as a generic pricing solver. We develop basic implementations of branch-and-price with pricing by domain-independent dynamic programming and show that they outperform a world-leading solver on static mixed integer programming formulations for seven problem classes.

Cutting-planes are one of the most important building blocks for solving large-scale integer programming (IP) problems to (near) optimality.