Regret (a) and Sharpe ratio (b) under the Rényi bound. (a) The line plot illustrates the cumulative regret across the 4000 iterations for each agent optimizing a particular Rényi bound. The $x$-axis denotes the iteration and $y$-axis the accompanying cumulative regret. (b) The line plot illustrates the average achieved Sharpe ratio of an agent across the 4000 iterations, for each particular Rényi bound. The $x$-axis denotes the iteration and $y$-axis the Sharpe ratio. Here, blue is for agents optimizing Rényi bound for $α→+∞$⁠, orange for $α=10$⁠, green for $α=2$⁠, red for $α→+1-$⁠, purple for $α=0.5$⁠, and brown for $α→0+$⁠. Dashed black line represents regret under a random policy (i.e., any arm). Each agent was simulated 20 times (95% confidence interval). In our simulations, the agents with $α→+1-$ and $α=2$ obtained the best performance.