Related papers: Non-commutative optimization problems with differe…
This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are not, in…
When optimizing real-time systems, designers often face a challenging problem where the schedulability constraints are non-convex, non-continuous, or lack an analytical form to understand their properties. Although the optimization…
In this paper we study various approaches for exploiting symmetries in polynomial optimization problems within the framework of semi definite programming relaxations. Our special focus is on constrained problems especially when the…
The synthesis problem for partially observable Markov decision processes (POMDPs) is to compute a policy that satisfies a given specification. Such policies have to take the full execution history of a POMDP into account, rendering the…
Partially observable Markov Decision Processes (POMDPs) are a standard model for agents making decisions in uncertain environments. Most work on POMDPs focuses on synthesizing strategies based on the available capabilities. However, system…
The Travelling Salesman Problem (TSP) is an important combinatorial optimisation problem, and is usually solved on a quantum computer using a Quadratic Unconstrained Binary Optimisation (QUBO) formulation or a Higher Order Binary…
It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show…
In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a…
This paper presents a constrained adaptive dynamic programming (CADP) algorithm to solve general nonlinear nonaffine optimal control problems with known dynamics. Unlike previous ADP algorithms, it can directly deal with problems with state…
Differentiable planning enables gradient-based optimization of decision-making problems by leveraging differentiable models of system dynamics. However, in highly nonlinear and hybrid discrete-continuous domains, the resulting optimization…
We present a memory-bounded optimization approach for solving infinite-horizon decentralized POMDPs. Policies for each agent are represented by stochastic finite state controllers. We formulate the problem of optimizing these policies as a…
Statistical inference problems arising within signal processing, data mining, and machine learning naturally give rise to hard combinatorial optimization problems. These problems become intractable when the dimensionality of the data is…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
We present a semidefinite program (SDP) algorithm to find eigenvalues of Schr\"{o}dinger operators within the bootstrap approach to quantum mechanics. The bootstrap approach involves two ingredients: a nonlinear set of constraints on the…
In this paper, we analyze the convergence of several discretize-then-optimize algorithms, based on either a second-order or a fourth-order finite difference discretization, for solving elliptic PDE-constrained optimization or optimal…
This paper addresses a quadratic problem with assignment constraints, an NP-hard combinatorial optimization problem arisen from facility location, multiple-input multiple-output detection, and maximum mean discrepancy calculation et al. The…
Automated machine learning aims to automate the whole process of machine learning, including model configuration. In this paper, we focus on automated hyperparameter optimization (HPO) based on sequential model-based optimization (SMBO).…
Markov Decision Problems (MDPs) provide a foundational framework for modelling sequential decision-making across diverse domains, guided by optimality criteria such as discounted and average rewards. However, these criteria have inherent…
Combinatorial optimization (CO) is the fundamental problem at the intersection of computer science, applied mathematics, etc. The inherent hardness in CO problems brings up challenge for solving CO exactly, making deep-neural-network-based…
Policy optimization (PO), an essential approach of reinforcement learning for a broad range of system classes, requires significantly more system data than indirect (identification-followed-by-control) methods or behavioral-based direct…