SlowGuess/NeurIPS_2023_OCR huggingface dataset:
We fine-tune the parameters of both algorithms and evaluate their performance in the following experimental setup: We fix the ambient dimension  $d = 80$ , the number of arms  $|\mathcal{X}| = 10000$ , and the number of rounds  $T = 50000$ . Both the unknown parameter vector,  $\theta^{*}$ , and the arm embeddings are sampled from a multivariate Gaussian distribution. Subsequently, the arm embeddings are shifted and normalized to ensure that all mean rewards are non-negative, with the maximum reward mean being set to 0.5. Upon pulling an arm, we observe a Bernoulli random variable with a probability corresponding to its mean reward.
In this experimental setting, we observe a significant performance advantage of LINNASH over Thompson Sampling. We plot our results in Figure 1, which shows that the Nash regret of LINNASH decreases notably faster than that of Thompson Sampling.
Another notable advantage of LINNASH evident from the experiments is due to successive elimination. The variance in the quality of arms pulled decreases as the number of rounds progresses – see Figures 2 and 3. This is due to the bulk elimination of suboptimal arms at regular intervals. In contrast, Thompson Sampling incurs a large variance in quality of arms being pulled even after several rounds, since no arms are being eliminated at any point.