We consider the problem of regret minimization in non-parametric stochastic bandits. When the rewards are known to be bounded from above, there exists asymptotically optimal algorithms, with asymptotic regret depending on an infi-mum of Kullback-Leibler divergences (KL).

We consider the problem of fitting variational posterior approximations using stochastic optimization methods.

The last equation is derived as follows. Inaddition, we set the observation varianceσx to 0.25. Logistic(;µ,s) is the density function of a logistic distribution with the location parameterµand the scale parameters,andσ isthe logistic sigmoid function. Before each activation, we apply the layer normalization [Ba et al., 2016] to stabilize training. When the model has sufficiently high expressive power,b may diverge to infinity [Rezende and Viola, 2018], so we add a regularization term of(b+2ζ( b))/m to the loss function, wherem is the number of training examples.