  Heavy ball momentum is crucial in accelerating (stochastic) gradient-based
optimization algorithms for machine learning. Existing heavy ball momentum is
usually weighted by a uniform hyperparameter, which relies on excessive tuning.
Moreover, the calibrated fixed hyperparameter may not lead to optimal
performance. In this paper, to eliminate the effort for tuning the
momentum-related hyperparameter, we propose a new adaptive momentum inspired by
the optimal choice of the heavy ball momentum for quadratic optimization. Our
proposed adaptive heavy ball momentum can improve stochastic gradient descent
(SGD) and Adam. SGD and Adam with the newly designed adaptive momentum are more
robust to large learning rates, converge faster, and generalize better than the
baselines. We verify the efficiency of SGD and Adam with the new adaptive
momentum on extensive machine learning benchmarks, including image
classification, language modeling, and machine translation. Finally, we provide
convergence guarantees for SGD and Adam with the proposed adaptive momentum.
