Before revision:  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 .
After revision:  Our algorithms automatically adapt to problem parameters such as smoothness .