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Planning under uncertainty requires complex reasoning about future events, and this complexity increases with the addition of multiple agents. One problem faced when considering multi-agent systems under uncertainty is the handling of shared resources. Adding a resource constraint limits the actions that agents can take, forcing collaborative decision making on who gets to use what resources. Prior work has considered different formulations, such as satisfying a resource constraint in expectation or ensuring that a resource constraint is met some percent of the time. However, these formulations of constrained planning ignore important distributional information about resource usage. Namely, they do not consider how bad the worst cases can get. In this paper, we formulate a risk-constrained shared resource problem and aim to limit the risk of excessive use of such resources. We focus on optimising for reward while constraining the Conditional Value-at-Risk (CVaR) of the shared resource. While CVaR is well studied in the single-agent setting, we consider the challenges that arise from the state and action space explosion in the multi-agent setting. In particular, we exploit risk contributions, a measure introduced in finance research which quantifies how much individual agents affect the joint risk. We present an algorithm that uses risk contributions to iteratively update single-agent policies until the joint risk constraint is satisfied. We evaluate our algorithm on two synthetic domains. |
