Abstract
Epistemic sets are a simple and efficient way of representing uncertain beliefs in AI, in which an agent identifies those states or worlds that she deems to be possible. We investigate their application to multi-agent distributed learning and decision making, in particular to best-of-n problems in which a population of agents must reach a consensus by identifying the best out of n possible alternatives or choices, each of different quality. We show that, despite their limited representational power, epistemic sets can be effectively deployed by agents engaged in a learning process in which they receive evidence directly from the environment and also pool or fuse their beliefs with those of other agents, in order to solve a best-of-n problem. We describe an analytical model of such a system based on ordinary differential equations and conduct a fixed point analysis so as to obtain insights into macro-level convergence properties. We then conduct a series of agent-based simulation experiments to investigate the robustness of the epistemic set approach. The results suggest that when applied to best-of-n problems epistemic sets are robust to noise and scalable to large state spaces, even when the population size is relatively small. This in turn supports the claim that they have potential applications in decentralised AI and swarm robotics at a range of different scales.
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Notes
- 1.
In some cases swarms alternate between periods of exploration and periods of pooling where for the latter they move to a common location to ensure mixing of different beliefs.
- 2.
We recognize that there are other possible approaches to updating in this context, especially when the agent’s belief is inconsistent with the evidence [10]. Here we simply adopt this updating method as one viable possibility.
- 3.
In other words, the only possible stable fixed points are \((x_1,\ldots ,x_7)=(0,0,0,0,1,0,0)\), (0, 0, 0, 0, 0, 1, 0) or (0, 0, 0, 0, 0, 0, 1) corresponding to \(x_{\{s_1\}}=1\), \(x_{\{s_2\}}=1\) and \(x_{\{s_3\}}=1\) respectively.
- 4.
Arguably in this case the agents are not strictly solving best-of-n since they may not be identifying the best choice but rather just choices of high quality.
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Acknowledgments
This work was funded and delivered in partnership between the Thales Group, University of Bristol and with the support of the UK Engineering and Physical Sciences Research Council, ref. EP/R004757/1 entitled “Thales-Bristol Partnership in Hybrid Autonomous Systems Engineering (T-B PHASE).”
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Lawry, J., Crosscombe, M., Harvey, D. (2019). Epistemic Sets Applied to Best-of-n Problems. In: Kern-Isberner, G., Ognjanović, Z. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2019. Lecture Notes in Computer Science(), vol 11726. Springer, Cham. https://doi.org/10.1007/978-3-030-29765-7_25
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