Predicting human behavior from a small amount of training examples is a challenging machine learning problem. In this thesis, we introduce the principle of maximum causal entropy, a general technique for applying information theory to decision-theoretic, game-theoretic, and control settings where relevant information is sequentially revealed over time. This approach guarantees decision-theoreti...

We consider the approximation of some optimal control problems for Navier-Stokes equation via a Dynamic Programming approach. These arise in many industrial applications and are very challenging from numerical point view since semi-discretization dynamics corresponds to an evolutive system ordinary differential equations high-dimension. The typical approach is based on Pontryagin maximum princi...

We consider the Bellman residual minimization approach for solving discounted Markov decision problems, where we assume that a generative model of the dynamics and rewards is available. At each policy iteration step, an approximation of the value function for the current policy is obtained by minimizing an empirical Bellman residual defined on a set of n states drawn i.i.d. from a distribution ...

We study numerical approximations for the payoff function of the stochastic optimal stopping and control problem. It is known that the payoff function of the optimal stopping and control problem corresponds to the solution of a normalized Bellman PDE. The principal aim of this thesis is to study the rate at which finite difference approximations, derived from the normalized Bellman PDE, converg...

In the spring of 2003, I began to wonder about the history of the Bellman-Ford algorithm [CLRS01] for finding shortest paths in a graph. In particular, I was interested in understanding when Bellman’s name and Ford’s name became jointly associated with the algorithm. To research these questions, I made trips to the BBN Technologies and MIT libraries, did Web searches, and sent emails to univers...

We study the Bellman equation for undiscounted exit time optimal control problems for nonlinear systems and nonnegative instantaneous costs using the dynamic programming approach. Using viscosity solution theory, we prove a uniqueness theorem that characterizes the value functions for these problems as the unique viscosity solutions of the corresponding Bellman equations that satisfy appropriat...

This article describes a class of jump-uncertain stochastic control systems, and derives an Itô–Liu formula with jump. We characterize optimal law, that satisfies the Hamilton–Jacobi–Bellman equation Then, this paper deduces portfolio game under uncertain financial markets The information players is symmetrical. market constituted risk-free asset risky whose price process subjected to Black–Sch...

We propose a novel stochastic extension of timed automata, i.e. Markovian Timed Automata (MTA). We study the problem of optimizing the reachability probabilities in this model. Two variants are considered, namely, the timebounded and unbounded reachability. In each case, we propose Bellman equations to characterize the probability. For the former, we provide two approaches to solve the Bellman ...

In this article, an efficient algorithm for an optimal decision strategy approximation is introduced. The proposed approximation of the Bellman equation is based on HDMR technique. This non-parametric function approximation is used not only to reduce memory demands necessary to store Bellman function, but also to allow its fast approximate minimization. On that account, a clear connection betwe...