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I was reading up on stochastic subgradient descent, and most sources i could find via google search give quick proofs on convergence in expectation and probability, and say that proofs of almost sure convergence exist.

Can anyone point me to a proof of this claim? I would be especially interested in proving the following claim : for $f$ convex and a decreasing sequence $\gamma_k$ of steps such that $\sum_{i=1}^{\infty} \gamma_i = \infty$, $\sum_{i=1}^{\infty} \gamma_i^2 < \infty$ we have $\lim_{k \rightarrow \infty} x_k = x^* $ almost surely, where $x_k$ is a sequence generated by stochastic subgradient descent.

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