相关论文: A Moment and Sum-of-Squares Extension of Dual Dyna…
This paper presents exact Semi-Definite Program (SDP) reformulations for infinite-dimensional moment optimization problems involving a new class of piecewise Sum-of-Squares (SOS)-convex functions and projected spectrahedral support sets.…
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 spaces, in a discrete-time infinite horizon…
Power systems that need to integrate renewables at a large scale must account for the high levels of uncertainty introduced by these power sources. This can be accomplished with a system of many distributed grid-level storage devices.…
Combining recent moment and sparse semidefinite programming (SDP) relaxation techniques, we propose an approach to find smooth approximations for solutions of problems involving nonlinear differential equations. Given a system of nonlinear…
Dynamic programming (DP) is an algorithmic design paradigm for the efficient, exact solution of otherwise intractable, combinatorial problems. However, DP algorithm design is often presented in an ad-hoc manner. It is sometimes difficult to…
Differential Dynamic Programming (DDP) is an efficient computational tool for solving nonlinear optimal control problems. It was originally designed as a single shooting method and thus is sensitive to the initial guess supplied. This work…
It is well-known that any sum of squares (SOS) program can be cast as a semidefinite program (SDP) of a particular structure and that therein lies the computational bottleneck for SOS programs, as the SDPs generated by this procedure are…
This paper develops a new storage-optimal algorithm that provably solves generic semidefinite programs (SDPs) in standard form. This method is particularly effective for weakly constrained SDPs. The key idea is to formulate an approximate…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…
Reach-avoid problems involve driving a system to a set of desirable configurations while keeping it away from undesirable ones. Providing mathematical guarantees for such scenarios is challenging but have numerous potential practical…
We present a novel, practical, and provable approach for solving diagonally constrained semi-definite programming (SDP) problems at scale using accelerated non-convex programming. Our algorithm non-trivially combines acceleration motions…
We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly…
This paper provides an overview, analysis, and comparison of second-order dynamic optimization algorithms, i.e., constrained Differential Dynamic Programming (DDP) and Sequential Quadratic Programming (SQP). Although a variety of these…
We present FilterDDP, a differential dynamic programming algorithm for solving discrete-time, optimal control problems (OCPs) with nonlinear equality constraints. Unlike prior methods based on merit functions or the augmented Lagrangian…
We consider a discounted infinite horizon optimal stopping problem. If the underlying distribution is known a priori, the solution of this problem is obtained via dynamic programming (DP) and is given by a well known threshold rule. When…
We study the convergence rate of moment-sum-of-squares hierarchies of semidefinite programs for optimal control problems with polynomial data. It is known that these hierarchies generate polynomial under-approximations to the value function…
We devise a scheme for solving an iterative sequence of linear programs (LPs) or second order cone programs (SOCPs) to approximate the optimal value of any semidefinite program (SDP) or sum of squares (SOS) program. The first LP and…
Multi-period mean-variance optimization is a long-standing problem, caused by the failure of dynamic programming principle. This paper studies the mean-variance optimization in a setting of finite-horizon discrete-time Markov decision…
Two-stage stochastic programming is a problem formulation for decision-making under uncertainty. In the first stage, the actor makes a best "here and now" decision in the presence of uncertain quantities that will be resolved in the future,…