Bayesian Ambiguity Contraction-based Adaptive Robust Markov Decision Processes for Adversarial Surveillance Missions
Organizations: University of Michigan, Ann Arbor, MI 48109, USA
Abstract
Collaborative Combat Aircraft (CCAs) are envisioned to enable autonomous Intelligence, Surveillance, and Reconnaissance (ISR) missions in contested environments, where adversaries may act strategically to deceive or evade detection. These missions pose challenges due to model uncertainty and the need for safe, real-time decision-making. Robust Markov Decision Processes (RMDPs) provide worst-case guarantees but are limited by static ambiguity sets that capture initial uncertainty without adapting to new observations. This paper presents an adaptive RMDP framework tailored to ISR missions with CCAs. We introduce a mission-specific formulation in which the CCA alternates between movement and sensing states. Adversarial uncertainty is represented by finite threat prototypes defining observation, exposure, and state-action transition models. Our approach incrementally refines policies by eliminating inconsistent threat models, allowing the CCA to move from worst-case protection toward more efficient mission policies while maintaining robustness. We establish fixed point stability, agreement with nominal planning as credible sets identify the true node-specific threat prototypes, and a conservative expected value guarantee while those prototypes remain credible. Experiments under Gaussian and non-Gaussian threat models across diverse network topologies show higher mission rewards and fewer exposure events compared to nominal and static robust planners.
Figures & tables
| Mission graph | |
| Surveillance node representing a physical location | |
| State space of the CCA RMDP | |
| Action space of the CCA | |
| Set of probability distributions over | |
| Finite set of candidate threat prototypes | |
| Candidate threat prototype |
| Credible Set | Transition Ambiguity Set | |
|---|---|---|
| Definition | Threat prototypes that remain plausible at node | Transition models induced by via |
| Uncertainty | Model uncertainty from limited observations | Transition uncertainty captured in the RMDP |
| Update | Shrinks from posterior updates and pruning | Contracts through |
| Usage | Determines remaining prototype hypotheses | Used in the robust Bellman operator |
| Parameter | Description | Value / Setting |
|---|---|---|
| Threat prototypes | 3 categories | |
| Sensing actions | 4 actions | |
| Observation model | Gaussian | |
| Exposure score model | Gaussian | |
| Exposure threshold | 0.5 | |
| Discount factor | 0.98 |
| Planner | Observation Reward | Cumulative Exposures | Total Reward |
|---|---|---|---|
| Adaptive Robust | 5882.44 168.12 | 39.13 11.19 | 9861.38 1345.84 |
| Nominal | 6780.49 108.32 | 240.92 65.92 | 4887.74 |
| Static Robust | 1487.82 233.79 | 89.64 9.16 | 190.63 858.26 |
| Parameter | Description | New Value / Setting |
|---|---|---|
| Observation model | Gaussian mixture or log-normal mixture | Mixed Gaussian / log-normal |
| Exposure score model | Gaussian mixture | Mixed Gaussian |
| Sensing cost | ||
| Immediate exposure weight | ||
| Persistent decay rate | ||
| Persistent exposure weight |
| Planner | Observation Reward | Cumulative Exposures | Total Reward |
|---|---|---|---|
| Adaptive Robust | 7334.50 936.78 | 77.29 26.41 | 4416.98 3101.26 |
| Nominal | 8414.99 1069.28 | 109.11 39.93 | 5352.14 |
| Static Robust | 3210.33 297.09 | 87.62 11.74 | 1505.94 |
| Graph Type | Nodes | Planner | Obs. Reward | Cum. Exposure | Total Reward |
|---|---|---|---|---|---|
| Barabasi-Albert | 15 | Adaptive Robust | 26604.09 ± 228.80 | 109.60 ± 7.17 | 64112.19 ± 1991.10 |
| Nominal | 27633.34 ± 215.70 | 474.80 ± 103.36 | 9686.63 ± 14999.06 | ||
| Static Robust | 6376.57 ± 676.51 | 365.00 ± 13.33 | 10969.77 ± 2855.34 | ||
| 30 | Adaptive Robust | 25267.94 ± 237.34 | 121.60 ± 4.25 | 155323.85 ± 1247.38 | |
| Nominal | 27355.98 ± 151.74 | 744.70 ± 123.64 | 70484.12 ± 13970.15 | ||
| Static Robust | 6234.28 ± 744.20 | 365.70 ± 14.01 | 105826.26 ± 2308.49 |
Robust Markov Decision Processes
Robust Markov decision processes optimize decisions under uncertain dynamics, seeking reliable performance against adverse transition models.
See all 25 papers