Variational inequalities with monotone operators  capture many problems of interest, notably convex optimization and convex-concave saddle point problems. Classical methods based on the MirrorProx algorithm require two operator evaluations per iteration, which is the dominant factor in the running time in many settings. Additionally, the algorithms typically require careful settings of the step sizes based on the parameters of the problems such as smoothness. In this work, we develop new algorithms addressing both of these shortcomings simultaneously. Our algorithms use a single operator evaluation per iteration and automatically adapt to  problem parameters such as smoothness . We show that our algorithms are universal and simultaneously achieve the optimal convergence rates in the non-smooth, smooth, and stochastic  settings.
We develop new adaptive algorithms for variational inequalities with monotone operators , which capture many problems of interest, notably convex optimization and convex-concave saddle point problems. Our algorithms automatically adapt to unknown problem parameters such as the smoothness and the norm of the operator, and the variance of the stochastic evaluation oracle . We show that our algorithms are universal and simultaneously achieve the optimal convergence rates in the non-smooth, smooth, and stochastic settings. The convergence guarantees of our algorithms improve over existing adaptive methods by a \Omega(\sqrt{\ln T settings.
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Variational
We develop new adaptive algorithms for variational
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, which
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Classical methods based on the MirrorProx algorithm require two operator evaluations per iteration, which is the dominant factor in the running time in many settings. Additionally, the algorithms typically require careful settings of the step sizes based on the parameters of the problems such as smoothness. In this work, we develop new algorithms addressing both of these shortcomings simultaneously. Our algorithms use a single operator evaluation per iteration and
Our algorithms
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unknown
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smoothness
the smoothness and the norm of the operator, and the variance of the stochastic evaluation oracle
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settings. The convergence guarantees of our algorithms improve over existing adaptive methods by a \Omega(\sqrt{\ln T