Auction-Based Scheduling

Many sequential decision-making tasks require satisfaction of multiple, partially contradictory objectives. Existing approaches are monolithic, namely all objectives are fulfilled using a single policy, which is a function that selects a sequence of actions. We present auction-based scheduling, a modular framework for multi-objective decision-making problems. Each objective is fulfilled using a separate policy, and the policies can be independently created, modified, and replaced. Understandably, different policies with conflicting goals may choose conflicting actions at a given time. In order to resolve conflicts, and compose policies, we employ a novel auction-based mechanism. We allocate a bounded budget to each policy, and at each step, the policies simultaneously bid from their available budgets for the privilege of being scheduled and choosing an action. Policies express their scheduling urgency using their bids and the bounded budgets ensure long-run scheduling fairness. We lay the foundations of auction-based scheduling using path planning problems on finite graphs with two temporal objectives. We present decentralized algorithms to synthesize a pair of policies, their initially allocated budgets, and bidding strategies. We consider three categories of decentralized synthesis problems, parameterized by the assumptions that the policies make on each other: (a) strong synthesis, with no assumptions and strongest guarantees, (b) assume-admissible synthesis, with weakest rationality assumptions, and (c) assume-guarantee synthesis, with explicit contract-based assumptions. For reachability objectives, we show that, surprisingly, decentralized assume-admissible synthesis is always possible when the out-degrees of all vertices are at most two.