Table 2 compares recent work on sparse linear bandits based on a number of important factors. Some of the mentioned bounds depend on problem-dependent parameters (e.g. Carpentier and Munos [ 2012 ] assume that the action set is a Euclidean ball, and that the noise is directly added to the parameter vector, i.e. In this setting, Carpentier and Munos [ 2012 ] present a O ( d p n) regret bound. Li et al. [ 2022 ] require a stronger condition This is generally not true, but may hold with high probability.

M different samples in parallel from the environment so that the reward for each agent is realized.

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Then,wecalculatethe mean stiffness of the value network across all state pairs and report its average computed over all trainingepochs. Eachagentis trained on 200 training levels for 25M environment steps. The mean and standard deviation are computedover10differentruns. Morespecifically,wecollect100 training episodes throughout the training and evaluate the value network prediction for the initial stateofeachtrajectory. Each agent is trained on 200 training levels for 25M environment steps.

Fortraining,PPOfirst collects trajectoriesτ using the old policy networkπθold right before the update.