Online learning is not always about memorizing everything. Since the future can be statistically very different from the past, a critical challenge is to gracefully forget the history while new data comes in. To formalize this intuition, we revisit the classical notion of discounted regret using recently developed techniques in adaptive online learning. Our main result is a new algorithm that adapts to the complexity of both the loss sequence and the comparator, improving the widespread non-adaptive algorithm - gradient descent with a constant learning rate. In particular, our theoretical guarantee does not require any structural assumption beyond convexity, and the algorithm is provably robust to suboptimal hyperparameter tuning. We further demonstrate such benefits through online conformal prediction, a downstream online learning task with set-membership decisions.

翻译：在线学习并非总是关于记忆一切。由于未来可能在统计上与过去大相径庭，一个关键的挑战是在新数据到来时优雅地遗忘历史。为了形式化这一直觉，我们利用最近在自适应在线学习中发展的技术，重新审视了经典的折扣遗憾概念。我们的主要成果是一种新算法，该算法能适应损失序列和比较器的复杂度，改进了广泛使用的非自适应算法——固定学习率的梯度下降。特别地，我们的理论保证在凸性之外无需任何结构性假设，且该算法对次优超参数调优具有鲁棒性。我们进一步通过在线共形预测（一种涉及集合成员决策的下游在线学习任务）展示了这些优势。