TDprop: Does adaptive optimization with Jacobi preconditioning help temporal difference learning?

We investigate whether Jacobi preconditioning, accounting for the bootstrap term in temporal difference (TD) learning, can help boost performance of adaptive optimizers. Our method, TDprop, computes a per-parameter learning rate based on the diagonal preconditioning of the TD update rule. We show how this can be used in both n-step returns and TD(?). Our theoretical findings demonstrate that including this additional preconditioning information is comparable to normal semi-gradient TD if the optimal learning rate is found for both via a hyperparameter search. This matches our experimental results. In Deep RL experiments using Expected SARSA, TDprop meets or exceeds the performance of Adam in all tested games under near-optimal learning rates, but a well-tuned SGD can yield similar performance in most settings. Our findings suggest that Jacobi preconditioning may improve upon Adam in Deep RL, but despite incorporating additional information from the TD bootstrap term, may not always be better than SGD. Moreover, they suggest that more theoretical investigations are needed to understand adaptive optimizers under optimal hyperparameter regimes in TD learning: simpler methods may, surprisingly, be theoretically comparable after a hyperparameter search.