Invariance-Based Dynamic Regret Minimization
This work addresses the problem of dynamic regret minimization in stochastic non-stationary linear bandits for applications where historical data may still carry partial information about the reward model.
The authors tackled the problem of stochastic non-stationary linear bandits, achieving significant regret improvements by leveraging invariances in the reward model, with sufficient historical data. The proposed algorithm, ISD-linUCB, reduces problem dimensionality, yielding better performance in fast-changing environments.
We consider stochastic non-stationary linear bandits where the linear parameter connecting contexts to the reward changes over time. Existing algorithms in this setting localize the policy by gradually discarding or down-weighting past data, effectively shrinking the time horizon over which learning can occur. However, in many settings historical data may still carry partial information about the reward model. We propose to leverage such data while adapting to changes, by assuming the reward model decomposes into stationary and non-stationary components. Based on this assumption, we introduce ISD-linUCB, an algorithm that uses past data to learn invariances in the reward model and subsequently exploits them to improve online performance. We show both theoretically and empirically that leveraging invariance reduces the problem dimensionality, yielding significant regret improvements in fast-changing environments when sufficient historical data is available.