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Uncertain optimization problems with decision dependent information discovery allow the decision maker to control the timing of information discovery, in contrast to the classic multistage setting where uncertain parameters are revealed…
As most robust combinatorial min-max and min-max regret problems with discrete uncertainty sets are NP-hard, research into approximation algorithm and approximability bounds has been a fruitful area of recent work. A simple and well-known…
Adaptively controlling and minimizing regret in unknown dynamical systems while controlling the growth of the system state is crucial in real-world applications. In this work, we study the problem of stabilization and regret minimization of…
In this paper, we consider a multistage expected utility maximization problem where the decision maker's utility function at each stage depends on historical data and the information on the true utility function is incomplete. To mitigate…
In this paper we extend the adaptive gradient descent (AdaGrad) algorithm to the optimal distributed control of parabolic partial differential equations with uncertain parameters. This stochastic optimization method achieves an improved…
Reducing the variance of the gradient estimator is known to improve the convergence rate of stochastic gradient-based optimization and sampling algorithms. One way of achieving variance reduction is to design importance sampling strategies.…
Dealing with uncertainty in optimization parameters is an important and longstanding challenge. Typically, uncertain parameters are predicted accurately, and then a deterministic optimization problem is solved. However, the decisions…
We present an optimisation-based method for synthesising a dynamic regret optimal controller for linear systems with potentially adversarial disturbances and known or adversarial initial conditions. The dynamic regret is defined as the…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…
We develop approximation algorithms for set-selection problems with deterministic constraints, but random objective values, i.e., stochastic probing problems. When the goal is to maximize the objective, approximation algorithms for probing…
Although nearly 20 years have passed since its conception, the feasibility pump algorithm remains a widely used heuristic to find feasible primal solutions to mixed-integer linear problems. Many extensions of the initial algorithm have been…
Bilevel Optimization Programming is used to model complex and conflicting interactions between agents, for example in Robust AI or Privacy-preserving AI. Integrating bilevel mathematical programming within deep learning is thus an essential…
This paper presents a scheme for dual robust control of batch processes under parametric uncertainty. The dual-control paradigm arises in the context of adaptive control. A trade-off should be decided between the control actions that…
We investigate online convex optimization in non-stationary environments and choose dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible…
This paper investigates a class of stochastic bilevel optimization problems where the upper-level function is nonconvex with potentially unbounded smoothness and the lower-level problem is strongly convex. These problems have significant…
This thesis investigates the design of algorithms for solving min-max optimization problems, which form the mathematical foundation of many modern applications in machine learning, game theory, and optimization. This work offers new…
Robust reinforcement learning (Robust RL) seeks to handle epistemic uncertainty in environment dynamics, but existing approaches often rely on nested min--max optimization, which is computationally expensive and yields overly conservative…
Mini-batch algorithms have been proposed as a way to speed-up stochastic convex optimization problems. We study how such algorithms can be improved using accelerated gradient methods. We provide a novel analysis, which shows how standard…
It is common practice to apply gradient-based optimization algorithms to numerically solve large-scale ODE constrained optimal control problems. Gradients of the objective function are most efficiently computed by approximate adjoint…
We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order Taylor models (with q >= 1) that have been recently…