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How to Exhibit More Predictable Behaviors

Salomé Lepers, Sophie Lemonnier, Vincent Thomas, Olivier Buffet

TL;DR

This paper designs reward functions for the agent which encode her goal to make next states or actions predictable by the observer; shows that these induced OAMDPs can be represented by goal-oriented or discounted MDPs; and analyzes the properties of the proposed reward functions theoretically.

Abstract

This paper looks at predictability problems, i.e., wherein an agent must choose its strategy in order to optimize the predictions that an external observer could make. We address these problems while taking into account uncertainties on the environment dynamics and on the observed agent's policy. To that end, we assume that the observer 1. seeks to predict the agent's future action or state at each time step, and 2. models the agent using a stochastic policy computed from a known underlying problem, and we leverage on the framework of observer-aware Markov decision processes (OAMDPs). We propose action and state predictability performance criteria through reward functions built on the observer's belief about the agent policy; show that these induced predictable OAMDPs can be represented by goal-oriented or discounted MDPs; and analyze the properties of the proposed reward functions both theoretically and empirically on two types of grid-world problems.

How to Exhibit More Predictable Behaviors

TL;DR

This paper designs reward functions for the agent which encode her goal to make next states or actions predictable by the observer; shows that these induced OAMDPs can be represented by goal-oriented or discounted MDPs; and analyzes the properties of the proposed reward functions theoretically.

Abstract

This paper looks at predictability problems, i.e., wherein an agent must choose its strategy in order to optimize the predictions that an external observer could make. We address these problems while taking into account uncertainties on the environment dynamics and on the observed agent's policy. To that end, we assume that the observer 1. seeks to predict the agent's future action or state at each time step, and 2. models the agent using a stochastic policy computed from a known underlying problem, and we leverage on the framework of observer-aware Markov decision processes (OAMDPs). We propose action and state predictability performance criteria through reward functions built on the observer's belief about the agent policy; show that these induced predictable OAMDPs can be represented by goal-oriented or discounted MDPs; and analyze the properties of the proposed reward functions both theoretically and empirically on two types of grid-world problems.
Paper Structure (38 sections, 2 theorems, 5 equations, 14 figures, 2 tables)

This paper contains 38 sections, 2 theorems, 5 equations, 14 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Markov Decision Processes
  4. Observer-Aware Markov Decision Processes
  5. Contribution
  6. Predictable Observer-Aware MDPs
  7. Belief Function and Properties of pOAMDPs
  8. pOAMDP Reward Function
  9. Reward Definition
  10. Valid SSPs?
  11. Generating and Interpreting Policies
  12. Protocol
  13. Maze problem
  14. Firefighter problem
  15. Baseline Policies
  16. ...and 23 more sections

Key Result

Proposition 1

Let us assume that Then the pOAMDP is a well-defined problem as its induced SSP satisfies assumptions (A1) and (A2).

Figures (14)

  • Figure 1: Agent in its environment and a passive observer
  • Figure 2: An OAMDP agent (3) assumes that the observer's expectation (2) is that the agent behaves so as to achieve some task (1).
  • Figure 3: Transition function of an ill-defined p-OASSP for state predictability, with transition probabilities as edge labels.
  • Figure 4: Action predictability results showing, for mazes $M_1$--$M_7$, the stochastic policy $\pi_\text{\sc mdp-s}$ (left) (which "covers" all deterministic policies $\pi_\text{\sc mdp-b}$) and the OAMDP policy $\pi^{\mathcal{A}}_\text{pred}$ (right). All policies have been computed using $\gamma=1$.
  • Figure 5: Results for maze $M_8$
  • ...and 9 more figures

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Proposition 2
  • proof