Both the human brain and artificial learning agents operating in real-world or comparably complex environments are faced with the challenge of online model selection. In principle this challenge can be overcome: hierarchical Bayesian inference provides a principled method for model selection and it converges on the same posterior for both off-line (i.e. batch) and online learning. However, maintaining a parameter posterior for each model in parallel has in general an even higher memory cost than storing the entire data set and is consequently clearly unfeasible. Alternatively, maintaining only a limited set of models in memory could limit memory requirements. However, sufficient statistics for one model will usually be insufficient for fitting a different kind of model, meaning that the agent loses information with each model change. We propose that episodic memory can circumvent the challenge of limited memory-capacity online model selection by retaining a selected subset of data points. We design a method to compute the quantities necessary for model selection even when the data is discarded and only statistics of one (or few) learnt models are available. We demonstrate on a simple model that a limited-sized episodic memory buffer, when the content is optimised to retain data with statistics not matching the current representation, can resolve the fundamental challenge of online model selection.
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