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.
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2026 2verdicts
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The iterates of the stochastic proximal gradient method converge almost surely and in mean to a minimizer without requiring boundedness or variance control on the random variables.
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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.
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Convergence of the Iterates of the Stochastic Proximal Gradient Method
The iterates of the stochastic proximal gradient method converge almost surely and in mean to a minimizer without requiring boundedness or variance control on the random variables.