A common feature of these applications is that there are multiple decision makers interacting with each other in a common environment.

In this paper, we explore two fundamental first-order algorithms in convex optimization, namely, gradient descent (GD) and proximal gradient method (ProxGD). Our focus is on making these algorithms entirely adaptive by leveraging local curvature information of smooth functions.

From the perspective of statistical learning theory, (1) is rather intriguing. Moreover, they do not provide instance-wise matching lower bounds to verify the tightness of the upper bounds.

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