ZOPPA at fixed positive temperature converges under minimal assumptions by acting as an exact proximal point method on a smoothed objective, with explicit connections back to the original function and convergence for its sampled version.
The first result we give is partly a consequence of these works, but we also establish the surjectivity of the zeroth-order proximal operator zproxδ λ,f
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Convergence of zeroth-order proximal point algorithms in the high-temperature regime
ZOPPA at fixed positive temperature converges under minimal assumptions by acting as an exact proximal point method on a smoothed objective, with explicit connections back to the original function and convergence for its sampled version.