Lookbehind Optimizer: k steps back, 1 step forward

The Lookahead optimizer improves the training stability of deep neural networks by having a set of fast weights that "look ahead" to guide the descent direction. Here, we combine this idea with sharpness-aware minimization (SAM) to stabilize its multi-step variant and improve the loss-sharpness trade-off. We propose Lookbehind, which computes $k$ gradient ascent steps ("looking behind") at each iteration and combine the gradients to bias the descent step toward flatter minima. We apply Lookbehind on top of two popular sharpness-aware training methods -- SAM and adaptive SAM (ASAM) -- and show that our approach leads to a myriad of benefits across a variety of tasks and training regimes. Particularly, we show increased generalization performance, greater robustness against noisy weights, and higher tolerance to catastrophic forgetting in lifelong learning settings.