Dice Question Streamline Icon: https://streamlinehq.com

Polynomial regret for learning bounded contracts with many actions

Ascertain whether online learning of bounded contracts against a fixed agent admits polynomial regret bounds when the number of actions is polynomial in the number of outcomes m; and characterize regret guarantees when the agent is sampled afresh in each round.

Information Square Streamline Icon: https://streamlinehq.com

Background

The survey presents polynomial regret bounds for learning bounded contracts when the action space is constant, and exponential lower bounds in general instances requiring exponentially many actions. It highlights two unresolved directions: extending polynomial regret to polynomially many actions and analyzing the case where a fresh agent is drawn each round.

Resolving these questions would clarify the feasibility of learning bounded contracts in richer, more realistic markets.

References

It remains an open question to prove (or disprove) that the problem admits a polynomial regret bound when the number of actions is polynomial in m. It is also open what the corresponding regret bounds are when the agent is sampled afresh in each round.

— Algorithmic Contract Theory: A Survey (2412.16384 - Duetting et al., 20 Dec 2024) in Section 6.2 (Improved Regret Bounds with a Small Number of Actions)