We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of uncontrollable contextual variables. We consider the setting where the context distribution is uncertain but known to lie within an ambiguity set defined as a ball in the Wasserstein distance. We propose a novel algorithm for Wasserstein Distributionally Robust Bayesian Optimization that can handle continuous context distributions while maintaining computational tractability. Our theoretical analysis combines recent results in self-normalized concentration in Hilbert spaces and finite-sample bounds for distributionally robust optimization to establish sublinear regret bounds that match state-of-the-art results. Through extensive comparisons with existing approaches on both synthetic and real-world problems, we demonstrate the simplicity, effectiveness, and practical applicability of our proposed method.

In this paper, we study the problem of online tracking in linear control systems, where the objective is to follow a moving target. Unlike classical tracking control, the target is unknown, non-stationary, and its state is revealed sequentially, thus, fitting the framework of online non-stochastic control. We consider the case of quadratic costs and propose a new algorithm, called predictive linear online tracking (PLOT). The algorithm uses recursive least squares with exponential forgetting to learn a time-varying dynamic model of the target. The learned model is used in the optimal policy under the framework of receding horizon control. We show the dynamic regret of PLOT scales with $\mathcal{O}(\sqrt{TV_T})$, where $V_T$ is the total variation of the target dynamics and $T$ is the time horizon. Unlike prior work, our theoretical results hold for non-stationary targets. We implement our online control algorithm on a real quadrotor, thus, showcasing one of the first successful applications of online control methods on real hardware.

In this paper, we study the statistical difficulty of learning to control linear systems. We focus on two standard benchmarks, the sample complexity of stabilization, and the regret of the online learning of the Linear Quadratic Regulator (LQR). Prior results state that the statistical difficulty for both benchmarks scales polynomially with the system state dimension up to system-theoretic quantities. However, this does not reveal the whole picture. By utilizing minimax lower bounds for both benchmarks, we prove that there exist non-trivial classes of systems for which learning complexity scales dramatically, i.e. exponentially, with the system dimension. This situation arises in the case of underactuated systems, i.e. systems with fewer inputs than states. Such systems are structurally difficult to control and their system theoretic quantities can scale exponentially with the system dimension dominating learning complexity. Under some additional structural assumptions (bounding systems away from uncontrollability), we provide qualitatively matching upper bounds. We prove that learning complexity can be at most exponential with the controllability index of the system, that is the degree of underactuation.

In this paper, we study concepts of sparsity in the max-plus algebra and apply them to the problem of multivariate convex regression. We show how to efficiently find sparse (containing many −∞ elements) approximate solutions to max-plus equations by leveraging notions from submodular optimization. Subsequently, we propose a novel method for piecewise-linear surface fitting of convex multivariate functions, with optimality guarantees for the model parameters and an approximately minimum number of affine regions.

This paper addresses the problem of cooperative object transportation by two nonholonomic wheeled robots, with the coordination relying exclusively on implicit communication. We implement a leader-follower scheme, considering compliant contact between the object and the follower. Only the leader has knowledge of the object's goal configuration. The follower employs force/torque measurements to keep the contact stable and align itself with the object. The control scheme of the follower is based on the prescribed performance methodology guaranteeing thus the satisfaction of certain predefined force/torque constraints. In this way, the overall system acts as a perturbed version of the nominal car-like model. As a result, the leader implements a discontinuous control scheme, that drives robustly the system arbitrarily close to the goal configuration. No explicit data is exchanged among the robots, thus reducing bandwidth and increasing robustness and stealthiness. Finally, the proposed method is experimentally validated using two Pioneer mobile robots interconnected with a rod.

In this paper, we study the decentralized control problem of a two-agent system under local goal specifications given as temporal logic formulas. The agents collaboratively carry an object in a leader-follower scheme and lack means to exchange messages on-line, i.e., to communicate explicitly. Specifically, we propose a decentralized control protocol and a leader re-election strategy that secure the accomplishment of both agents' local goal specifications. The challenge herein lies in exploiting exclusively implicit inter-robot communication that is a natural outcome of the physical interaction of the robots with the object. An illustrative experiment is included clarifying and verifying the approach.

This paper addresses the problem of cooperative object manipulation with the coordination relying solely on implicit communication. We consider a decentralized leader-follower architecture where the leading robot, that has exclusive knowledge of the object's desired trajectory, tries to achieve the desired tracking behavior via an impedance control law. On the other hand, the follower estimates the leader's desired motion via a novel prescribed performance estimation law, that drives the estimation error to an arbitrarily small residual set, and implements a similar impedance control law. Both control schemes adopt feedback linearization as well as load sharing among the robots according to their specific payload capabilities. The feedback relies exclusively on each robot's force/torque, position as well as velocity measurements and apart from a few commonly predetermined constant parameters, no explicit data is exchanged on-line among the robots, thus reducing the required communication bandwidth and increasing robustness. Finally, a comparative simulation study clarifies the proposed method and verifies its efficiency.