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Thompson Sampling with Less Exploration is Fast and Optimal

ICML 2023 · Bandits and online learning › Contextual bandits and Thompson sampling · approach: Thompson sampling analysis

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Reduce exploration: sample from posterior only with prob. 1/K, greedy on empirical mean otherwise (ε-TS) vs. full TSThompson Sampling · Table 2, Bernoulli K=10 and K=50, Gaussian K=10 and K=50 (running time)average running time (s): 0.25 → 0.11 (K=10); 0.98 → 0.27 (K=50)Helped
Replace ExpTS+ KL-inverse sampling with ε-TS posterior sampling at ε=1/KExpTS+ · Table 2, Bernoulli (running time)average running time (s): 43 → 0.11 (K=10); 38 → 0.27 (K=50)Helped
Reduced exploration (ε=1/K) in ε-TSGaussian rewards · Table 2, Gaussian K=10 (running time)average running time (s): ε-TS 0.11 vs ExpTS+ 0.15No clear effect
Set ε=1/K in ε-TSε-TS · Figure 1 regret, K=10 and K=50 (Bernoulli, Gaussian, Poisson, Gamma)cumulative regretHelped
Set ε=1/K in ε-TS vs ExpTS+ (regret)ε-TS · Figure 1, Bernoulli and Gamma (K=10); Gaussian and Gamma (K=50)cumulative regretNo clear effect
Set ε=1/K in ε-TS vs ExpTS+ (regret, Poisson and Bernoulli K=50)ε-TS · Figure 1, Gaussian and Poisson (K=10); Bernoulli and Poisson (K=50)cumulative regretHelped
Use ε=1/K sampling instead of full TS (ε=1) with posterior samplingThompson Sampling · Theory: worst-case regret bound for Gaussian, Bernoulli, Poisson, Gammaworst-case regret bound order: O(√(KT log K)) with ε=1 (within √log K of minimax) vs. minimax optimal with ε=1/KHelped

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