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Inference-time controllable generation is essential for real-world applications of unconditional diffusion models. However, most existing techniques focus on individual samples, struggling in applications that require the sample population…
We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their…
This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time…
This paper is devoted to distributed continuous-time and discrete-time optimization problems with nonuniform convex constraint sets and nonuniform stepsizes for general differentiable convex objective functions. The communication graphs are…
Many real-world systems often involve physical components or operating environments with highly nonlinear and uncertain dynamics. A number of different control algorithms can be used to design optimal controllers for such systems, assuming…
In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a…
We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…
We investigate an optimization problem that arises when working within the paradigm of Data-Driven Computational Mechanics. In the context of the diffusion-reaction problem, such an optimization problem seeks for the continuous primal…
Reinforcement learning (RL) struggles to scale to large, combinatorial action spaces common in many real-world problems. This paper introduces a novel framework for training discrete diffusion models as highly effective policies in these…
This papers shows the convergence of optimal control problems where the constraint function is discretised by a particle method. In particular, we investigate the viscous Burgers equation in the whole space $\mathbb R$ by using…
Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…
We first show that the discounted cost, cost up to an exit time, and ergodic cost involving controlled non-degenerate diffusions are continuous on the space of stationary control policies when the policies are given a topology introduced by…
In this work we adapt a prediction-correction algorithm for continuous time-varying convex optimization problems to solve dynamic programs arising from Model Predictive Control. In particular, the prediction step tracks the evolution of the…
This paper considers the problem of designing time-dependent, real-time control policies for controllable nonlinear diffusion processes, with the goal of obtaining maximally-informative observations about parameters of interest. More…
This paper extends algorithms that remove the fixed point bias of decentralized gradient descent to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint…
We study reinforcement learning in hybrid discrete-continuous action spaces, such as settings where the discrete component selects a regime (or index) and the continuous component optimizes within it -- a structure common in robotics,…
We tackle the issue of finding a good policy when the number of policy updates is limited. This is done by approximating the expected policy reward as a sequence of concave lower bounds which can be efficiently maximized, drastically…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
We present an algorithm for the approximation of a finite horizon optimal control problem for advection-diffusion equations. The method is based on the coupling between an adaptive POD representation of the solution and a Dynamic…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…