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Surprise-based learning allows agents to rapidly adapt to non-stationarystochastic environments characterized by sudden changes. We show that exactBayesian inference in a hierarchical model gives rise to a surprise-modulatedtrade-off between forgetting old observations and integrating them with the newones. The modulation depends on a probability ratio, which we call "BayesFactor Surprise", that tests the prior belief against the current belief. Wedemonstrate that in several existing approximate algorithms the Bayes FactorSurprise modulates the rate of adaptation to new observations. We derive threenovel surprised-based algorithms, one in the family of particle filters, one inthe family of variational learning, and the other in the family of messagepassing, that have constant scaling in observation sequence length andparticularly simple update dynamics for any distribution in the exponentialfamily. Empirical results show that these surprise-based algorithms estimateparameters better than alternative approximate approaches and reach levels ofperformance comparable to computationally more expensive algorithms. The BayesFactor Surprise is related to but different from Shannon Surprise. In twohypothetical experiments, we make testable predictions for physiologicalindicators that dissociate the Bayes Factor Surprise from Shannon Surprise. Thetheoretical insight of casting various approaches as surprise-based learning,as well as the proposed online algorithms, may be applied to the analysis ofanimal and human behavior, and to reinforcement learning in non-stationaryenvironments.

Learning in Volatile Environments with the Bayes Factor Surprise