Related papers: Dynamic programming approach to principal-agent pr…
We consider stochastic model predictive control of a multi-agent systems with constraints on the probabilities of inter-agent collisions. We first study a sample-based approximation of the collision probabilities and use this approximation…
We consider the problem of controlling the movement of multiple cooperating agents so as to minimize an uncertainty metric associated with a finite number of targets. In a one-dimensional mission space, we adopt an optimal control framework…
The problem of order execution is cast as a relative entropy-regularized robust optimal control problem in this article. The order execution agent's goal is to maximize an objective functional associated with his profit-and-loss of trading…
We study the optimal stopping problem of McKean-Vlasov diffusions when the criterion is a function of the law of the stopped process. A remarkable new feature in this setting is that the stopping time also impacts the dynamics of the…
Ensuring robust decision-making in multi-agent systems is challenging when agents have distinct, possibly conflicting objectives and lack full knowledge of each other's strategies. This is apparent in safety-critical applications such as…
We explore how to build a vector field from the various functions involved in a given mathematical program, and show that locally-stable equilibria of the underlying dynamical system are precisely the local solutions of the optimization…
Cooperatively planning for multiple agents has been proposed as a promising method for strategic and motion planning for automated vehicles. By taking into account the intent of every agent, the ego agent can incorporate future interactions…
In the theory of dynamic programming, an optimal policy is a policy whose lifetime value dominates that of all other policies from every possible initial condition in the state space. This raises a natural question: when does optimality…
Consider the problem of minimizing the expected value of a (possibly nonconvex) cost function parameterized by a random (vector) variable, when the expectation cannot be computed accurately (e.g., because the statistics of the random…
In a noncooperative dynamic game, multiple agents operating in a changing environment aim to optimize their utilities over an infinite time horizon. Time-varying environments allow to model more realistic scenarios (e.g., mobile devices…
Although dynamic games provide a rich paradigm for modeling agents' interactions, solving these games for real-world applications is often challenging. Many real-world interactive settings involve general nonlinear state and input…
We present an algorithm, based on the Differential Dynamic Programming framework, to handle trajectory optimization problems in which the horizon is determined online rather than fixed a priori. This algorithm exhibits exact one-step…
Principal-agent problems arise when one party acts on behalf of another, leading to conflicts of interest. The economic literature has extensively studied principal-agent problems, and recent work has extended this to more complex scenarios…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
We consider the 0-1 Penalized Knapsack Problem (PKP). Each item has a profit, a weight and a penalty and the goal is to maximize the sum of the profits minus the greatest penalty value of the items included in a solution. We propose an…
We present a new, tractable method for solving and analyzing risk-aware control problems over finite and infinite, discounted time-horizons where the dynamics of the controlled process are described as a martingale problem. Supposing…
In recent years, information relaxation and duality in dynamic programs have been studied extensively, and the resulted primal-dual approach has become a powerful procedure in solving dynamic programs by providing lower-upper bounds on the…
In this work, we proposed a new dynamic distributed planning approach that is able to take into account the changes that the agent introduces on his set of actions to be planned in order to take into account the changes that occur in his…
We consider discrete-time infinite horizon deterministic optimal control problems with nonnegative cost per stage, and a destination that is cost-free and absorbing. The classical linear-quadratic regulator problem is a special case. Our…
Game theory serves as a powerful tool for distributed optimization in multi-agent systems in different applications. In this paper we consider multi-agent systems that can be modeled by means of potential games whose potential function…