Related papers: No-regret optimization of time-varying bilevel pro…
Motivated by the increasing attention to overall social benefits in networked multi-agent systems, this paper investigates an optimization problem building on noncooperative games under high-level regulation, which can be formulated in a…
We consider Bayesian optimization using Gaussian Process models, also referred to as kernel-based bandit optimization. We study the methodology of exploring the domain using random samples drawn from a distribution. We show that this random…
We develop a non-parametric, data-driven, tractable approach for solving multistage stochastic optimization problems in which decisions do not affect the uncertainty. The proposed framework represents the decision variables as elements of a…
We consider the problem of designing an allocation rule or an "online learning algorithm" for a class of bandit problems in which the set of control actions available at each time $s$ is a convex, compact subset of $\mathbb{R}^d$. Upon…
This paper proposes a linear bandit algorithm that is adaptive to environments at two different levels of hierarchy. At the higher level, the proposed algorithm adapts to a variety of types of environments. More precisely, it achieves…
Model Predictive Control (MPC) is a common tool for the control of nonlinear, real-world systems, such as legged robots. However, solving MPC quickly enough to enable its use in real-time is often challenging. One common solution is given…
We study the non-stationary stochastic multiarmed bandit (MAB) problem and propose two generic algorithms, namely, the limited memory deterministic sequencing of exploration and exploitation (LM-DSEE) and the Sliding-Window Upper Confidence…
Achieving sample efficiency in online episodic reinforcement learning (RL) requires optimally balancing exploration and exploitation. When it comes to a finite-horizon episodic Markov decision process with $S$ states, $A$ actions and…
Under data distributions which may be heavy-tailed, many stochastic gradient-based learning algorithms are driven by feedback queried at points with almost no performance guarantees on their own. Here we explore a modified "anytime…
Many safety-critical real-world problems, such as autonomous driving and collaborative robots, are of a distributed multi-agent nature. To optimize the performance of these systems while ensuring safety, we can cast them as distributed…
Bilevel optimization problems, encountered in fields such as economics, engineering, and machine learning, pose significant computational challenges due to their hierarchical structure and constraints at both upper and lower levels.…
This paper presents a convex optimization-based solution to the design of state-feedback controllers for solving the linear quadratic regulator (LQR) problem of uncertain discrete-time systems with multiplicative noise. To synthesize a…
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…
We propose techniques for approximating bilevel optimization problems with non-smooth lower level problems that can have a non-unique solution. To this end, we substitute the expression of a minimizer of the lower level minimization problem…
Bilevel linear programming (LP) is one of the simplest classes of bilevel optimization problems, yet it is known to be NP-hard in general. Specifically, determining whether the optimal objective value of a bilevel LP is at least as good as…
We consider estimation and control in linear time-varying dynamical systems from the perspective of regret minimization. Unlike most prior work in this area, we focus on the problem of designing causal estimators and controllers which…
Bilevel optimization deals with nested problems in which a leader takes the first decision to minimize their objective function while accounting for a follower's best-response reaction. Constrained bilevel problems with integer variables…
When the lower-level optimal solution set-valued mapping of a bilevel optimization problem is not single-valued, we are faced with an ill-posed problem, which gives rise to the optimistic and pessimistic bilevel optimization problems, as…
This paper reviews gradient-based techniques to solve bilevel optimization problems. Bilevel optimization is a general way to frame the learning of systems that are implicitly defined through a quantity that they minimize. This…
Bayesian optimization is a sample-efficient method for solving expensive, black-box optimization problems. Stochastic programming concerns optimization under uncertainty where, typically, average performance is the quantity of interest. In…