Active Learning for Efficient Sampling of Control Models of Collectives

Many large-scale systems benefit from an organizational structure to provide for problem decomposition. A pivotal problem solving setting is given by hierarchical control systems familiar from hierarchical task networks. If these structures can be modified autonomously by, e.g., Coalition formation and reconfiguration, adequate decisions on higher levels require a faithful abstracted model of a collective of agents. An illustrative example is found in calculating schedules for a set of power plants organized in a hierarchy of Autonomous Virtual Power Plants. Functional dependencies over the combinatorial domain, such as the joint costs or rates of change of power production, are approximated by repeatedly sampling input-output pairs and substituting the actual functions by piecewise linear functions. However, if the sampled data points are weakly informative, the resulting abstracted high-level optimization introduces severe errors. Furthermore, obtaining additional point labels amounts to solving computationally hard optimization problems. Building on prior work, we propose to apply techniques from active learning to maximize the information gained by each additional point. Our results show that significantly better allocations in terms of cost-efficiency (up to 33.7 % reduction in costs in our case study) can be found with fewer but carefully selected sampling points using Decision Forests.