Peter Richtarik outlines multi-agent block-coordinate optimization with verified merges

peter_richtarik · x · 2026-10-22

Optimization researcher Peter Richtarik describes a multi-agent parallel optimization scheme: each agent owns one block of a shared solution and searches a corrected local objective that accounts for its impact on all other blocks. Each epoch runs four steps — parallel private search (H steps per agent), verification of every proposal on the global loss, coloring of the dependency graph (κ colors) so blocks sharing terms can't interfere, and merging the highest-gain non-interfering group. The guaranteed inequality F(x^{k+1}) ≤ F(x^k) − (Σ gb)/κ means a verified merge never worsens the shared solution.

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