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Increasing the Value of Information During Planning in Uncertain Environments

Gaurab Pokharel

TL;DR

This work addresses the undervaluation of information-gathering actions in online POMDP planning under long information delays. It introduces POMCPe, an entropy-enhanced extension of POMCP that adds an entropy-derived term to the UCB1-inspired heuristic to favor high-voi trajectories without sacrificing anytime planning. Empirical tests on the Long Hallway domain show that POMCPe substantially improves cumulative rewards and the likelihood of obtaining informative observations, though it can increase total decision time in larger problems. The approach advances practical planning in uncertain environments by more accurately trading off immediate task rewards against long-horizon information value, with future work on broader domain testing and theoretical analysis.

Abstract

Prior studies have demonstrated that for many real-world problems, POMDPs can be solved through online algorithms both quickly and with near optimality. However, on an important set of problems where there is a large time delay between when the agent can gather information and when it needs to use that information, these solutions fail to adequately consider the value of information. As a result, information gathering actions, even when they are critical in the optimal policy, will be ignored by existing solutions, leading to sub-optimal decisions by the agent. In this research, we develop a novel solution that rectifies this problem by introducing a new algorithm that improves upon state-of-the-art online planning by better reflecting on the value of actions that gather information. We do this by adding Entropy to the UCB1 heuristic in the POMCP algorithm. We test this solution on the hallway problem. Results indicate that our new algorithm performs significantly better than POMCP.

Increasing the Value of Information During Planning in Uncertain Environments

TL;DR

This work addresses the undervaluation of information-gathering actions in online POMDP planning under long information delays. It introduces POMCPe, an entropy-enhanced extension of POMCP that adds an entropy-derived term to the UCB1-inspired heuristic to favor high-voi trajectories without sacrificing anytime planning. Empirical tests on the Long Hallway domain show that POMCPe substantially improves cumulative rewards and the likelihood of obtaining informative observations, though it can increase total decision time in larger problems. The approach advances practical planning in uncertain environments by more accurately trading off immediate task rewards against long-horizon information value, with future work on broader domain testing and theoretical analysis.

Abstract

Prior studies have demonstrated that for many real-world problems, POMDPs can be solved through online algorithms both quickly and with near optimality. However, on an important set of problems where there is a large time delay between when the agent can gather information and when it needs to use that information, these solutions fail to adequately consider the value of information. As a result, information gathering actions, even when they are critical in the optimal policy, will be ignored by existing solutions, leading to sub-optimal decisions by the agent. In this research, we develop a novel solution that rectifies this problem by introducing a new algorithm that improves upon state-of-the-art online planning by better reflecting on the value of actions that gather information. We do this by adding Entropy to the UCB1 heuristic in the POMCP algorithm. We test this solution on the hallway problem. Results indicate that our new algorithm performs significantly better than POMCP.
Paper Structure (15 sections, 1 theorem, 16 equations, 4 figures, 3 tables, 3 algorithms)

This paper contains 15 sections, 1 theorem, 16 equations, 4 figures, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. POMDP Definition
  4. Offline vs. Online Planning
  5. Policy Trees
  6. POMCP
  7. The Problem
  8. Long Hallway Domain
  9. The Solution
  10. Results and Discussion
  11. Experimental Setup
  12. Comparing POMCP and POMCPe
  13. Evaluating with Larger Hallways
  14. Conclusion and Future Work
  15. Acknowledgements

Key Result

Proposition 4.1

Given, at time $t$ the entropy $H_n$, the size of particle filter $n$, and the count of particles in the state that received the new particle $c_x$, the entropy at time $t+1$ can be calculated as:

Figures (4)

  • Figure 1: A policy tree. Each Circular node corresponds to a belief and each triangular node corresponds to an action taken in the belief above it
  • Figure 2: The Long Hallway problem. $k_2$ determines how long from the start until the agent can gather important information in the small horizontal hallway (where the agent can observe which hallway it is in) and $k_1$ controls the time between when information is collected and when it is used
  • Figure : Where $\eta = \frac{1}{Pr(o \mid b, a)}$ is a normalizing constant with $Pr(o \mid b, a) = \sum_{s' \in S} O(o \mid s', a) \sum_{s \in S} T(s' \mid s, a) \cdot b(s)$. $s'$ is the state at time step $t+1$ and $s$ at $t$.
  • Figure : Where $\eta = \frac{1}{Pr(o \mid b, a)}$ is a normalizing constant with $Pr(o \mid b, a) = \sum_{s' \in S} O(o \mid s', a) \sum_{s \in S} T(s' \mid s, a) \cdot b(s)$. $s'$ is the state at time step $t+1$ and $s$ at $t$.

Theorems & Definitions (2)

  • Proposition 4.1
  • proof