Kirby Banman

Kirby Banman, Liam Peet-Pare, Nidhi Hegde et al.

Most convergence guarantees for stochastic gradient descent with momentum (SGDm) rely on iid sampling. Yet, SGDm is often used outside this regime, in settings with temporally correlated input samples such as continual learning and reinforcement learning. Existing work has shown that SGDm with a decaying step-size can converge under Markovian temporal correlation. In this work, we show that SGDm under covariate shift with a fixed step-size can be unstable and diverge. In particular, we show SGDm under covariate shift is a parametric oscillator, and so can suffer from a phenomenon known as resonance. We approximate the learning system as a time varying system of ordinary differential equations, and leverage existing theory to characterize the system's divergence/convergence as resonant/nonresonant modes. The theoretical result is limited to the linear setting with periodic covariate shift, so we empirically supplement this result to show that resonance phenomena persist even under non-periodic covariate shift, nonlinear dynamics with neural networks, and optimizers other than SGDm.

Yangchen Pan, Kirby Banman, Martha White

Recent work has shown that sparse representations -- where only a small percentage of units are active -- can significantly reduce interference. Those works, however, relied on relatively complex regularization or meta-learning approaches, that have only been used offline in a pre-training phase. In this work, we pursue a direction that achieves sparsity by design, rather than by learning. Specifically, we design an activation function that produces sparse representations deterministically by construction, and so is more amenable to online training. The idea relies on the simple approach of binning, but overcomes the two key limitations of binning: zero gradients for the flat regions almost everywhere, and lost precision -- reduced discrimination -- due to coarse aggregation. We introduce a Fuzzy Tiling Activation (FTA) that provides non-negligible gradients and produces overlap between bins that improves discrimination. We first show that FTA is robust under covariate shift in a synthetic online supervised learning problem, where we can vary the level of correlation and drift. Then we move to the deep reinforcement learning setting and investigate both value-based and policy gradient algorithms that use neural networks with FTAs, in classic discrete control and Mujoco continuous control environments. We show that algorithms equipped with FTAs are able to learn a stable policy faster without needing target networks on most domains.