Abstract: Some embodiments are directed to a computer-implemented method of interacting with a physical environment according to a policy. The policy determines multiple action probabilities of respective actions based on an observable state of the physical environment. The policy includes a neural network parameterized by a set of parameters. The neural network determines the action probabilities by determining a final layer input from an observable state and applying a final layer of the neural network to the final layer input. The final layer is applied by applying a linear combination of a set of equivariant base weight matrices to the final layer input. The base weight matrices are equivariant in the sense that, for a set of multiple predefined transformations of the final layer input, each transformation causes a corresponding predefined action permutation of the base weight matrix output for the final layer input.

Abstract: Some embodiments are directed to a computer-implemented method of interacting with a physical environment according to a policy. The policy determines multiple action probabilities of respective actions based on an observable state of the physical environment. The policy includes a neural network parameterized by a set of parameters. The neural network determines the action probabilities by determining a final layer input from an observable state and applying a final layer of the neural network to the final layer input. The final layer is applied by applying a linear combination of a set of equivariant base weight matrices to the final layer input. The base weight matrices are equivariant in the sense that, for a set of multiple predefined transformations of the final layer input, each transformation causes a corresponding predefined action permutation of the base weight matrix output for the final layer input.