Abstract

Scenario Approach to Robust Minmax Optimization — Caveats and New Results.
Debasish Chatterjee (IIT Bombay)

We shall discuss the so-called scenario approach, a popular probabilistic approximation method for robust minmax optimization problems via independent and identically distributed (i.i.d) sampling from the uncertainty set, from various perspectives. The scenario approach is well-studied in the important case of convex robust optimization problems. We will first examine how the phenomenon of concentration of measures affects the i.i.d sampling aspect of the scenario approach in high dimensions and its relation with the optimal values. If time permits, a few important and new results on both the asymptotic behaviour (consistency) and finite time behaviour of the scenario approach in the more general setting of nonconvex minmax optimization problems will be mentioned. In the direction of the asymptotic behaviour of the scenario approach, we shall present an obstruction to consistency that arises when the decision set is noncompact. In the direction of finite sample guarantees, we shall discuss a general methodology for extracting `probably approximately correct’ type estimates for the finite sample behaviour of the scenario approach for a large class of nonconvex problems. The results are reported at length in https://arxiv.org/abs/1906.01476

Output Synchronisation for Area Coverage with Robots
Srikant Sukumar (IIT Bombay)

The area coverage problem requires that a finite set of mobile robot sensors position themselves in an environmentto ensure optimal sensing of a phenomenon in the region. This requires coverage of the entire convex set and also a higher densityof sensors in regions with larger probability of the phenomenon. We connect the solution of this problem to that of outputsynchronization of a network of agents. The output cost corresponds to the optimal coverage cost. The algorithms developed are distributedand therefore amenable to local implementation. We develop results for a network of Euler-Lagrange systems (typical models for mobile robots).