The Stochastic Gap: A Markovian Framework for Pre-Deployment Reliability and Oversight-Cost Auditing in Agentic Artificial Intelligence
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915891168411648 |
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| author | Pal, Biplab Bhattacharya, Santanu |
| author_facet | Pal, Biplab Bhattacharya, Santanu |
| contents | Agentic artificial intelligence (AI) in organizations is a sequential decision problem constrained by reliability and oversight cost. When deterministic workflows are replaced by stochastic policies over actions and tool calls, the key question is not whether a next step appears plausible, but whether the resulting trajectory remains statistically supported, locally unambiguous, and economically governable. We develop a measure-theoretic Markov framework for this setting. The core quantities are state blind-spot mass B_n(tau), state-action blind mass B^SA_{pi,n}(tau), an entropy-based human-in-the-loop escalation gate, and an expected oversight-cost identity over the workflow visitation measure.
We instantiate the framework on the Business Process Intelligence Challenge 2019 purchase-to-pay log (251,734 cases, 1,595,923 events, 42 distinct workflow actions) and construct a log-driven simulated agent from a chronological 80/20 split of the same process. The main empirical finding is that a large workflow can appear well supported at the state level while retaining substantial blind mass over next-step decisions: refining the operational state to include case context, economic magnitude, and actor class expands the state space from 42 to 668 and raises state-action blind mass from 0.0165 at tau=50 to 0.1253 at tau=1000. On the held-out split, m(s) = max_a pi-hat(a|s) tracks realized autonomous step accuracy within 3.4 percentage points on average.
The same quantities that delimit statistically credible autonomy also determine expected oversight burden. The framework is demonstrated on a large-scale enterprise procurement workflow and is designed for direct application to engineering processes for which operational event logs are available. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24582 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Stochastic Gap: A Markovian Framework for Pre-Deployment Reliability and Oversight-Cost Auditing in Agentic Artificial Intelligence Pal, Biplab Bhattacharya, Santanu Artificial Intelligence I.2.11; I.2.6; J.1 Agentic artificial intelligence (AI) in organizations is a sequential decision problem constrained by reliability and oversight cost. When deterministic workflows are replaced by stochastic policies over actions and tool calls, the key question is not whether a next step appears plausible, but whether the resulting trajectory remains statistically supported, locally unambiguous, and economically governable. We develop a measure-theoretic Markov framework for this setting. The core quantities are state blind-spot mass B_n(tau), state-action blind mass B^SA_{pi,n}(tau), an entropy-based human-in-the-loop escalation gate, and an expected oversight-cost identity over the workflow visitation measure. We instantiate the framework on the Business Process Intelligence Challenge 2019 purchase-to-pay log (251,734 cases, 1,595,923 events, 42 distinct workflow actions) and construct a log-driven simulated agent from a chronological 80/20 split of the same process. The main empirical finding is that a large workflow can appear well supported at the state level while retaining substantial blind mass over next-step decisions: refining the operational state to include case context, economic magnitude, and actor class expands the state space from 42 to 668 and raises state-action blind mass from 0.0165 at tau=50 to 0.1253 at tau=1000. On the held-out split, m(s) = max_a pi-hat(a|s) tracks realized autonomous step accuracy within 3.4 percentage points on average. The same quantities that delimit statistically credible autonomy also determine expected oversight burden. The framework is demonstrated on a large-scale enterprise procurement workflow and is designed for direct application to engineering processes for which operational event logs are available. |
| title | The Stochastic Gap: A Markovian Framework for Pre-Deployment Reliability and Oversight-Cost Auditing in Agentic Artificial Intelligence |
| topic | Artificial Intelligence I.2.11; I.2.6; J.1 |
| url | https://arxiv.org/abs/2603.24582 |