An analytical trust modulation method using prediction interval width for decentralized online convex optimization

Decentralized online convex optimization with coupled constraints provides a natural framework for networked resource allocation, demand response, and multi-agent control. Forecasts can improve performance, but most decentralized algorithms use forecast uncertainty only as a diagnostic rather than as a control input. This paper studies a local trust-modulation mechanism that maps prediction-interval width into the weight assigned to an optimistic gradient inside a decentralized primal–dual update. Narrow intervals imply higher trust, whereas wide intervals reduce optimism and may trigger a safe fallback. For a benchmark-aligned scalar positive-part surrogate, we derive a master primal–dual inequality and resulting bounds on dynamic regret and cumulative constraint violation with explicit dependence on weighted interval width, miscoverage, comparator variation, and network mixing. Empirically, a fully causal benchmark over sixteen non-overlapping quarterly electricity-load windows from 2011 to 2014 shows that the UQ-aware controller attains lower mean dynamic regret than the ex ante causal error-adaptive safeguard (141.046 ± 22.110 versus 144.033 ± 23.141), with a mean paired regret gap of −2.987 and a mean violation gap of +3.130. Under forecast corruption, the method degrades more gracefully than the other predictive baselines, although the safe no-prediction mode becomes best under severe corruption. A post-hoc behavior-matched width-blind diagnostic narrows the incremental gap sharply, indicating that the width-specific effect beyond generic conservativeness is modest in the scalar positive-part setting studied here.