Jointly lifting the curse of dimensionality and curse of history in I-POMDPs using interactive beliefs

Ascertain whether extensions of interactive belief–based methods, such as Interactive Particle Filtering (I-PF) or Interactive Point-based Value Iteration (I-PBVI), can simultaneously overcome both the curse of dimensionality and the curse of history when solving interactive partially observable Markov decision processes (I-POMDPs).

Background

I-POMDPs face three major computational obstacles: the curse of dimensionality due to interactive beliefs over states and other agents’ beliefs, the curse of history from exponential policy growth with horizon, and the curse of nested reasoning. Prior approximations address these issues separately—e.g., I-PF targets dimensionality, while I-PBVI targets history—but neither lifts both simultaneously.

The authors explicitly state uncertainty about whether interactive belief methods can be extended to jointly address both curses, suggesting this is a fundamental open question in the design of scalable, intention-aware planning algorithms for non-cooperative multi-agent settings.

References

Using interactive beliefs, it is therefore not known whether it is even possible to jointly lift both curses, for example, by extending I-PF or I-PBVI.

— Interactive POMDP Lite: Towards Practical Planning to Predict and Exploit Intentions for Interacting with Self-Interested Agents (1304.5159 - Hoang et al., 2013) in Section 1 Introduction