Symbolic regression in dynamic scenarios with gradually changing targets

Abstract Symbolic regression is a machine learning task: given a training dataset with features and targets, find a symbolic function that best predicts the target given the features. This paper concentrates on dynamic regression tasks, i.e. tasks where the goal changes during the model fitting process. Our study is motivated by dynamic regression tasks originating in the domain of reinforcement learning: we study four dynamic symbolic regression problems related to well-known reinforcement learning benchmarks, with data generated from the standard Value Iteration algorithm. We first show that in these problems the target function changes gradually, with no abrupt changes. Even these gradual changes, however, are a challenge to traditional Genetic Programming-based Symbolic Regression algorithms because they rely only on expression manipulation and selection. To address this challenge, we present an enhancement to such algorithms suitable for dynamic scenarios with gradual changes, namely the recently introduced type of leaf nodes called Linear Combination of Features. This type of leaf node, aided by the error backpropagation technique known from artificial neural networks, enables the algorithm to better fit the data by utilizing the error gradient to its advantage rather than searching blindly using only the fitness values. This setup is compared with a baseline of the core algorithm without any of our improvements and also with a classic evolutionary dynamic optimization technique: hypermutation. The results show that the proposed modifications greatly improve the algorithm ability to track a gradually changing target.