Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

How to Solve Contextual Goal-Oriented Problems with Offline Datasets?

Ying Fan, Jingling Li, Adith Swaminathan, Aditya Modi, Ching-An Cheng

TL;DR

The paper tackles offline Contextual Goal-Oriented (CGO) problems, where the context selects a goal set and rewards are sparse. It introduces CODA, a method that builds an action-augmented MDP by adding a fictitious action to jointly leverage unlabeled dynamics data and context-goal pairs, turning them into a fully labeled offline dataset. Under standard realizability, completeness, and concentrability assumptions, CODA plus a pessimistic offline RL backbone provably learns near-optimal policies without negative samples. Empirically, CODA outperforms reward-learning and goal-prediction baselines across diverse CGO relationships using AntMaze benchmarks, indicating strong potential for scalable offline CGO.

Abstract

We present a novel method, Contextual goal-Oriented Data Augmentation (CODA), which uses commonly available unlabeled trajectories and context-goal pairs to solve Contextual Goal-Oriented (CGO) problems. By carefully constructing an action-augmented MDP that is equivalent to the original MDP, CODA creates a fully labeled transition dataset under training contexts without additional approximation error. We conduct a novel theoretical analysis to demonstrate CODA's capability to solve CGO problems in the offline data setup. Empirical results also showcase the effectiveness of CODA, which outperforms other baseline methods across various context-goal relationships of CGO problem. This approach offers a promising direction to solving CGO problems using offline datasets.

How to Solve Contextual Goal-Oriented Problems with Offline Datasets?

TL;DR

The paper tackles offline Contextual Goal-Oriented (CGO) problems, where the context selects a goal set and rewards are sparse. It introduces CODA, a method that builds an action-augmented MDP by adding a fictitious action to jointly leverage unlabeled dynamics data and context-goal pairs, turning them into a fully labeled offline dataset. Under standard realizability, completeness, and concentrability assumptions, CODA plus a pessimistic offline RL backbone provably learns near-optimal policies without negative samples. Empirically, CODA outperforms reward-learning and goal-prediction baselines across diverse CGO relationships using AntMaze benchmarks, indicating strong potential for scalable offline CGO.

Abstract

We present a novel method, Contextual goal-Oriented Data Augmentation (CODA), which uses commonly available unlabeled trajectories and context-goal pairs to solve Contextual Goal-Oriented (CGO) problems. By carefully constructing an action-augmented MDP that is equivalent to the original MDP, CODA creates a fully labeled transition dataset under training contexts without additional approximation error. We conduct a novel theoretical analysis to demonstrate CODA's capability to solve CGO problems in the offline data setup. Empirical results also showcase the effectiveness of CODA, which outperforms other baseline methods across various context-goal relationships of CGO problem. This approach offers a promising direction to solving CGO problems using offline datasets.
Paper Structure (51 sections, 14 theorems, 56 equations, 7 figures, 5 tables, 1 algorithm)

This paper contains 51 sections, 14 theorems, 56 equations, 7 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Offline RL.
  4. Data-sharing in RL
  5. Preliminaries
  6. CGO Setup
  7. Infinite-horizon Formulation for CGO setup
  8. Offline Learning for CGO
  9. Contextual Goal-Oriented Data Augmentation (CODA)
  10. Action-Augmented MDP
  11. Policy conversion.
  12. Regret equivalence.
  13. Method
  14. Interpretation.
  15. CGO is Learnable with Positive Data Only
  16. ...and 36 more sections

Key Result

Theorem 4.1

The regret of a policy extended to the augmented MDP is equal to the regret of the policy in the original MDP, and any policy defined in the augmented MDP can be converted into that in the original MDP without increasing the regret. Thus, solving the augmented MDP can yield correspondingly optimal p

Figures (7)

  • Figure 1: Illustration of CODA: We create fictitious transitions from goal examples to terminal states under the given context in the action-augmented MDP with reward 1, which enables the supervised signal to propagate back to unsupervised transitions via Bellman equation.
  • Figure 2: Illustration of the context-goal relationship with increasing complexity (Each red boundary defines a goal set with its center location as context). (a) Contexts and goal sets are very similar such that it could be approximately solved by a context-agnostic policy. (b) Contexts are finite, and different contexts map to distinct goal sets, which requires context-dependent policies. (c) Contexts are continuous and infinite. The context-goal mapping is neither one-to-many nor many-to-one, creating a CGO problem with full complexity.
  • Figure 3: Reward model evaluation for the large-diverse dataset for original AntMaze environment. Green dots are outliers.
  • Figure 4: Reward model evaluation for the medium-diverse dataset for the original AntMaze environment. Green dots are outliers.
  • Figure 5: Reward model evaluation for the umaze-diverse dataset for the original AntMaze environment. Green dots are outliers.
  • ...and 2 more figures

Theorems & Definitions (30)

  • Theorem 4.1: Informal
  • Remark 4.2
  • Remark 4.3
  • Definition 5.3
  • Theorem 5.4
  • Remark 5.5
  • Remark 5.6
  • Remark A.1
  • Lemma A.2
  • Proposition A.3
  • ...and 20 more