Rich Sutton

Khurram Javed, Haseeb Shah, Rich Sutton et al.

Constructing states from sequences of observations is an important component of reinforcement learning agents. One solution for state construction is to use recurrent neural networks. Back-propagation through time (BPTT), and real-time recurrent learning (RTRL) are two popular gradient-based methods for recurrent learning. BPTT requires complete trajectories of observations before it can compute the gradients and is unsuitable for online updates. RTRL can do online updates but scales poorly to large networks. In this paper, we propose two constraints that make RTRL scalable. We show that by either decomposing the network into independent modules or learning the network in stages, we can make RTRL scale linearly with the number of parameters. Unlike prior scalable gradient estimation algorithms, such as UORO and Truncated-BPTT, our algorithms do not add noise or bias to the gradient estimate. Instead, they trade off the functional capacity of the network for computationally efficient learning. We demonstrate the effectiveness of our approach over Truncated-BPTT on a prediction benchmark inspired by animal learning and by doing policy evaluation of pre-trained policies for Atari 2600 games.

Khurram Javed, Martha White, Rich Sutton

Structural credit assignment for recurrent learning is challenging. An algorithm called RTRL can compute gradients for recurrent networks online but is computationally intractable for large networks. Alternatives, such as BPTT, are not online. In this work, we propose a credit-assignment algorithm -- \algoname{} -- that approximates the gradients for recurrent learning in real-time using $O(n)$ operations and memory per-step. Our method builds on the idea that for modular recurrent networks, composed of columns with scalar states, it is sufficient for a parameter to only track its influence on the state of its column. We empirically show that as long as connections between columns are sparse, our method approximates the true gradient well. In the special case when there are no connections between columns, the $O(n)$ gradient estimate is exact. We demonstrate the utility of the approach for both recurrent state learning and meta-learning by comparing the estimated gradient to the true gradient on a synthetic test-bed.