A Risk-Budget-Based DevOps Framework for Reliable Deployment of Non-Deterministic and AI-Enabled Systems

Abstract

We develop a mathematically rigorous risk-budget framework for the reliable deployment of AI-enabled non-deterministic systems across three canonical DevOps pipeline stages. Classical DevOps pipelines model software as deterministic finite automata; however, AI-enabled systems are stochastic processes on a probability space (Ω,F,P), and their deployment safety cannot be characterised by Boolean properties alone. We formalise deployment risk through coherent risk measures, specifically Conditional Value-at-Risk (CVaRα), and prove that among all coherent functionals dominating expected loss for log-concave distributions, CVaRα is the tightest, justifying its adoption as the canonical deployment risk measure. The associated risk-budget allocation problem is proved to admit a unique closed-form solution, in which the budget Rtotal is distributed as Ri = WiRtotal/∑jWj , the unique global minimiser of a weighted least-squares convex programme. A composite stage-weight function Wi = ασ2 i +β κi +γφi encodes loss variance σ 2 i , configurational complexity κi , and regulatory compliance exposure φi ; we prove that the resulting allocation operator R is monotone increasing in each risk component, scale invariant under rescaling of (α,β, γ), and sub-additive in the weighted risk sense, guaranteeing that the allocation responds predictably to changes in the pipeline risk profile. The DevOps pipeline is modelled as a discrete-time stochastic feedback control system, and a Lyapunov stability theorem is proved showing that the closed-loop state satisfies a mean-square bound that decays geometrically to a finite asymptotic noise floor determined by the system disturbance covariance, enabling practitioners to set performance service-level agreements from first principles. We further prove that model drift, formalised as the Kullback-Leibler divergence between the operational and training distributions, induces a risk increment bounded by M p DKL/2 via Pinsker’s inequality, yielding the certified retraining trigger DKL ≥ 2(Ltol/M) 2 that guarantees the generalisation error remains within prescribed tolerance Ltol at all times. Five theorems, four lemmas, and three corollaries with complete proofs constitute the mathematical core of this work. Empirical validation on an AI-enabled cloud security platform yields a 30% reduction in deployment time, a 25% reduction in critical failures, a 40% improvement in performance efficiency, and a 42.8% reduction in CVaR0.95 relative to the strongest reported baseline, outperforming all three state-of-the-art comparison frameworks across every reported metric.