Regularized Diffusion Adaptation via Conjugate Smoothing

The purpose of this work is to develop and study a decentralized strategy for Pareto optimization an aggregate cost consisting regularized risks. Each risk modeled as the expectation some loss function with unknown probability distribution while regularizers are assumed deterministic, but not required be differentiable or even continuous. individual, regularized, functions distributed across strongly-connected network agents optimal solution sought by appealing multi-agent diffusion strategy. To end, smoothed means infimal convolution it shown that approximate, smooth problem can made arbitrarily close original, non-smooth problem. Performance bounds established under conditions weaker than before in literature, hence applicable broader class adaptation learning problems.