The Stochastic Gap: A Markovian Framework for Pre-Deployment Reliability and Oversight-Cost Auditing in Agentic Artificial Intelligence

Biplab Pal; Santanu Bhattacharya

cs.AIMar 25, 2026

The Stochastic Gap: A Markovian Framework for Pre-Deployment Reliability and Oversight-Cost Auditing in Agentic Artificial Intelligence

Authors: Biplab Pal, Santanu Bhattacharya

Organizations: CARDS (Center for Real-Time Distributed Sensing and Autonomy), University of Maryland Baltimore County, Baltimore, MD, USA · Massachusetts Institute of Technology, Cambridge, MA, USA

Abstract

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.

Figures & tables

Context	Observed issue	Why it matters here
Air Canada chatbot [ 1 ]	Customer-facing chatbot provided incorrect fare guidance; liability attached to the enterprise rather than to the model artifact.	Reliability failures propagate into legal and governance risk.
McDonald’s–IBM drive-through pilot [ 2 ]	Large-scale voice-ordering pilot ended after mixed results and repeated ordering errors.	Sequential operational reliability, not one-shot fluency, governs real deployment.
Gartner 2025 agentic-AI forecast [ 3 ]	Over 40% of agentic-AI projects projected to be canceled because of escalating costs, unclear value, or inadequate risk controls.	Reliability and cost must be analyzed jointly rather than separately.
IBM 2025 ROI guidance [ 4 ]	Only 25% of AI initiatives reported as delivering expected ROI; only 16% scaled enterprise-wide.	Human oversight and integration cost can dominate the business case.

Table 1: Motivating industry evidence for a joint reliability-and-cost framing of agentic artificial intelligence.

Figure 1: Markov reliability model for scoped autonomy in enterprise workflows. A workflow state is mapped to an action through policy

\pi(a_{t}\mid s_{t})

, the process evolves under transition kernel

P(s_{t+1}\mid s_{t},a_{t})

, and a human-in-the-loop (HITL) gate escalates states with inadequate support, high branching entropy, or elevated risk.

Figure 2: Dominant empirical transitions in the BPI 2019 purchase-to-pay process. Edge widths are proportional to empirical transition probabilities. The log contains recurrent loops and exception-handling branches; the mean case length is 6.34 events, the 99th percentile is 24 events, the maximum observed case length is 990, and the transition-level self-loop rate is 15.7%.

Abstraction	States	SA pairs	$B_{n}(200)$	$B_{n}(1000)$	$B^{SA}_{\pi,n}(200)$	$B^{SA}_{\pi,n}(1000)$
Activity only	42	498	0.0004	0.0021	0.0077	0.0324
Activity + item type + GR	190	1217	0.0020	0.0212	0.0194	0.0681
Activity + item type + GR + value + actor	668	3262	0.0108	0.0460	0.0462	0.1253

Table 2: State refinement and blind mass on the full BPI 2019 log. Coarse state occupancy can appear well covered even when materially under-supported regions persist at the state-action layer.

Figure 3: Coverage on the full BPI 2019 log. (A) State blind-spot mass

\hat{B}_{n}(\tau)

remains modest even under refined state abstractions. (B) State-action blind mass

\hat{B}^{SA}_{\pi,n}(\tau)

increases substantially faster, particularly once value and actor context are included. The dashed red curve reports the corresponding risk-weighted blind mass for the refined transition model.

Figure 4: Scoped autonomy on the full BPI 2019 log under the refined state abstraction with

N(s)\geq 50

and

w(s)\leq 0.6

. Event-level autonomy remains substantially higher than end-to-end case-level autonomy because local ambiguity compounds along the trajectory.

$h_{0}$	$\widetilde{m}_{\mathrm{step}}$	$m_{\mathrm{step}}^{\mathrm{test}}$	$\widetilde{R}_{\mathrm{safe}}$	$R_{\mathrm{safe}}^{\mathrm{test}}$	$C_{0}^{\mathrm{test}}$	touches/case
1.50	0.721	0.684	0.520	0.556	0.033	3.02
2.00	0.675	0.637	0.404	0.496	0.161	2.26
2.25	0.654	0.615	0.354	0.452	0.231	1.90

Table 3: Held-out agent validation on the chronological 80/20 split of BPI 2019 under the refined state abstraction, with

\tau=50

and

w_{0}=0.6

\widetilde{R}_{\mathrm{safe}}

is the theoretical surrogate from Eq. ( 24 );

R_{\mathrm{safe}}^{\mathrm{test}}

is the realized safe completion with human fallback from Eq. ( 29 );

C_{0}^{\mathrm{test}}

is realized zero-touch completion from Eq. ( 28 ).

Figure 5: Theory-versus-agent comparison on the chronological held-out split of BPI 2019. (A) Theoretical autonomous-step surrogate

m(s)=\max_{a}\hat{\pi}(a\mid s)

versus realized held-out step accuracy as the entropy threshold

h_{0}

varies, with mean absolute gap 3.4 percentage points. (B) Reliability-cost frontier induced by the same gate: the x-axis is mean human touches per case, the y-axis is safe case completion, and the theoretical curve is conservative but monotone relative to the held-out agent.

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