2,767 research outputs found
Efficient Regret Minimization in Non-Convex Games
We consider regret minimization in repeated games with non-convex loss
functions. Minimizing the standard notion of regret is computationally
intractable. Thus, we define a natural notion of regret which permits efficient
optimization and generalizes offline guarantees for convergence to an
approximate local optimum. We give gradient-based methods that achieve optimal
regret, which in turn guarantee convergence to equilibrium in this framework.Comment: Published as a conference paper at ICML 201
Optimization, Learning, and Games with Predictable Sequences
We provide several applications of Optimistic Mirror Descent, an online
learning algorithm based on the idea of predictable sequences. First, we
recover the Mirror Prox algorithm for offline optimization, prove an extension
to Holder-smooth functions, and apply the results to saddle-point type
problems. Next, we prove that a version of Optimistic Mirror Descent (which has
a close relation to the Exponential Weights algorithm) can be used by two
strongly-uncoupled players in a finite zero-sum matrix game to converge to the
minimax equilibrium at the rate of O((log T)/T). This addresses a question of
Daskalakis et al 2011. Further, we consider a partial information version of
the problem. We then apply the results to convex programming and exhibit a
simple algorithm for the approximate Max Flow problem
- …