Randomized Exploration for Non-Stationary Stochastic Linear Bandits

We investigate two perturbation approaches to overcome conservatism that optimism based algorithms chronically suffer from in practice. The first approach replaces optimism with a simple randomization when using confidence sets. The second one adds random perturbations to its current estimate before maximizing the expected reward. For non-stationary linear bandits, where each action is associated with a d-dimensional feature and the unknown parameter is time-varying with total variation BT, we propose two randomized algorithms, Discounted Randomized LinUCB (D-RandLinUCB) and Discounted Linear Thompson Sampling (D-LinTS) via the two perturbation approaches. We highlight the statistical optimality versus computational efficiency trade-off between them in that the former asymptotically achieves the optimal dynamic regret tildeO(d7/8 BT1/4T3/4), but the latter is oracle-efficient with an extra logarithmic factor in the number of arms compared to minimax-optimal dynamic regret. In a simulation study, both algorithms show outstanding performance in tackling conservatism issue that Discounted LinUCB struggles with.