Research map / Bandits and online learning / Online convex optimization and games
Online Learning in Stackelberg Games with an Omniscient Follower
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Have an omniscient follower best-respond rather than letting the leader control the follower action | Linear Stackelberg game · Worst-case linear Stackelberg game | regret: \cR(T) \gtrsim T^{{(d-4)}/{(d-2)}} | Hurt |
| Use observed follower responses to imitate the follower | Imitation-based example · Imitation-based example | regret: \cR_{UCB}(T) \lesssim \sigma_b^2 \log T \cdot(d +\log T) versus \Omega(\sigma_b d\sqrt{T}) | Helped |
| Use the observed response to restrict exploration to the well-conditioned action set | UCB in the expert-guided example · Expert-guided exploration (strong reduction) | regret: \widetilde{\bO}(d\sqrt{T}) | Helped |
| Observe the follower response and use it to reduce the action set | \mathsf{Alg} in the expert-guided example · Expert-guided exploration (weak reduction) | regret: \bO\big((C_\zeta^d T^{d+1})^{\frac{1}{d+2}}\big) | Helped |
| Use the follower response as a proxy reward | \mathsf{Alg} in the polynomial bandit example · Polynomial bandit example | sample complexity: \widetilde{\bO}(d^{2k-1}/\epsilon^2) versus \widetilde{\bO}(d^{2k}/\epsilon^2) | Helped |
| Use traditional Eluder UCB instead of a tailored proxy-regret algorithm | Polynomial bandit example · Polynomial bandit example | sample complexity: \widetilde{\bO}(d^{2k}/\epsilon^2) rather than \widetilde{\bO}(d^{2k-1}/\epsilon^2) | Hurt |
| Choose an interior action a = 0 that reveals the true parameter | Leader in the failure-of-optimism example · Failure of optimism example | rounds to identify optimal action: one round | Helped |
| Use an optimism-based method such as UCB instead of the informative interior action | Leader in the failure-of-optimism example · Failure of optimism example | learning efficiency | Hurt |
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