  Most of the literature on learning in games has focused on the restrictive
setting where the underlying repeated game does not change over time. Much less
is known about the convergence of no-regret learning algorithms in dynamic
multiagent settings. In this paper, we characterize the convergence of
optimistic gradient descent (OGD) in time-varying games. Our framework yields
sharp convergence bounds for the equilibrium gap of OGD in zero-sum games
parameterized on natural variation measures of the sequence of games, subsuming
known results for static games. Furthermore, we establish improved second-order
variation bounds under strong convexity-concavity, as long as each game is
repeated multiple times. Our results also apply to time-varying general-sum
multi-player games via a bilinear formulation of correlated equilibria, which
has novel implications for meta-learning and for obtaining refined
variation-dependent regret bounds, addressing questions left open in prior
papers. Finally, we leverage our framework to also provide new insights on
dynamic regret guarantees in static games.
