Related papers: Finite adaptability in two-stage robust optimizati…

In this paper, we study the portfolio optimization problem with general utility functions and when the return and volatility of underlying asset are slowly varying. An asymptotic optimal strategy is provided within a specific class of…

Recent work by Mania et al. has proved that certainty equivalent control achieves nearly optimal regret for linear systems with quadratic costs. However, when parameter uncertainty is large, certainty equivalence cannot be relied upon to…

Contextual stochastic optimization is an advanced methodology to model uncertainty in the presence of contextual information during decision planning processes. Although classical methodologies focus on minimizing the expectation of a…

The presented work addresses two-stage stochastic programs (2SPs), a broadly applicable model to capture optimization problems subject to uncertain parameters with adjustable decision variables. In case the adjustable or second-stage…

Adaptive gradient methods like AdaGrad are widely used in optimizing neural networks. Yet, existing convergence guarantees for adaptive gradient methods require either convexity or smoothness, and, in the smooth setting, only guarantee…

This note presents a method that provides optimal monotone conditional error functions for a large class of adaptive two stage designs. The presented method builds on a previously developed general theory for optimal adaptive two stage…

This paper tackles the challenging problem of finding global optimal solutions for two-stage stochastic programs with continuous decision variables and nonconvex recourse functions. We introduce a two-phase approach. The first phase…

Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered…

In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast…

Reachability analysis is an important method in providing safety guarantees for systems with unknown or uncertain dynamics. Due to the computational intractability of exact reachability analysis for general nonlinear, high-dimensional…

This paper presents a novel transformation-proximal bundle algorithm for multistage adaptive robust optimization problems. By partitioning recourse decisions into state and control decisions, the proposed algorithm applies affine control…

Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference…

To integrate strategic, tactical and operational decisions, the two-stage optimization has been widely used to guide dynamic decision making. In this paper, we study the two-stage stochastic programming for complex systems with unknown…

The fixed template Promise Constraint Satisfaction Problem (PCSP) is a recently proposed significant generalization of the fixed template CSP, which includes approximation variants of satisfiability and graph coloring problems. All the…

We consider a general class of two-stage distributionally robust optimization (DRO) problems where the ambiguity set is constrained by fixed marginal probability laws that are not necessarily discrete. We derive primal and dual formulations…

Robust optimization methods have shown practical advantages in a wide range of decision-making applications under uncertainty. Recently, their efficacy has been extended to multi-period settings. Current approaches model uncertainty either…

Despite the numerous advances, reinforcement learning remains away from widespread acceptance for autonomous controller design as compared to classical methods due to lack of ability to effectively tackle the reality gap. The reliance on…

This paper presents a novel numerical optimisation method for infinite dimensional optimisation. The functional optimisation makes minimal assumptions about the functional and without any specific knowledge on the derivative of the…

We present a theoretical analysis of stochastic optimization methods in terms of their sensitivity with respect to the step size. We identify a key quantity that, for each method, describes how the performance degrades as the step size…

This paper discusses the stabilizability, weak stabilizability, exact observability and robust quadratic stabilizability of linear stochastic control systems. By means of the spectrum technique of the generalized Lyapunov operator, a…