Imagining Goals with Geometric Horizon Models for Policy Generalization

1Mila 2Université de Montréal 3Google DeepMind

†Equal Advising

Abstract

Training from offline data has allowed for substantial progress in domains such as robotics, leading to general-purpose policies that can be easily applied zero-shot or efficiently finetuned for downstream tasks. However, these policies can still have poor generalization, both due to the choice of modeling objective and from learning from a static dataset. In this work, we focus on the challenging task of zero-shot goal generalization, where a policy is evaluated on unseen tasks that require combining its existing knowledge (compositional generalization). An avenue for improving a policy's generalization is by generating new experience with world models; however, such generation has proven difficult for longer horizons. Thus, to alleviate this issue, we propose TD-Aug, which samples from a geometric horizon model and allows for directly imagining novel outcomes that can be achieved by composing existing knowledge. We demonstrate that training on these future outcomes as goals for goal-conditioned BC policies significantly improves generalization in stitching-based OGBench tasks.

Overview

Overview of TD-Aug. We a) train a GHM on an offline dataset to approximate samples from the successor measure of the behavior mixture policy. Then, b) we train BC policies on a mix of ground-truth and generated goals, improving zero-shot generalization on compositional tasks:

A geometric horizon model generates future states conditioned on a state and action. These predictions become goals for a behavior-cloning policy.

TD-Aug generates goals through a GHM that samples likely future states (s+), conditioned on the current state and action via Mβ(· | s, a). The GHM stitches across trajectories, predicting which outcomes are likely when composing behavior starting from different actions:

Short ground-truth trajectories from the pointmaze-giant training dataset.
Ground-truth trajectories from the dataset.
MCHC TD-Flow sample generation over 10 flow steps, with five outlined initial states and action arrows. Each query and its samples share a color.
Samples generated by a GHM (TD-Flow), conditioned on each outlined initial state and action.

Results

Results on OGBench “stitch” tasks. TD-Aug enables BC trained on short trajectories or atomic tasks to generalize to long-horizon, composite goals.

pointmaze-giant-stitch

Training data

Superimposed training trajectories

GCFBC

Task 2: navigate from bottom right to top left
(task success 0%, overall success 0%)

TD-Aug (MCHC)

Task 2: navigate from bottom right to top left
(task success 70%, overall success 54%)

puzzle-4x4-stitch

Training data

Individual training trajectories

GCFBC

Task 5: turn all buttons red
(task success 0%, overall success 0%)

TD-Aug (MCHC)

Task 5: turn all buttons red
(task success 34%, overall success 40%)

cube-triple-stitch

Training data

Individual training trajectories

GCFBC

Task 3: unstack and relocate all three cubes
(task success 0%, overall success 20%)

TD-Aug (MCHC)

Task 3: unstack and relocate all three cubes
(task success 25%, overall success 31%)

Seed-0 demonstrations for each policy pair. Success rates average three checkpoints per seed, then three seeds.

Quantitative Results

Table 1. Generalization on pointmaze stitching datasets. Success rate (%).
pointmazeGCFBC+ Cluster-Aug+ Dyn-Aug+ MC-Aug+ TD-Aug2+ TD-AugGCIQLQRLCRLHIQL
pointmaze-medium-stitch55 ± 1089 ± 594 ± 670 ± 296 ± 199 ± 074 ± 188 ± 54 ± 271 ± 8
pointmaze-large-stitch26 ± 662 ± 851 ± 1028 ± 1740 ± 397 ± 340 ± 189 ± 150 ± 018 ± 4
pointmaze-giant-stitch0 ± 03 ± 60 ± 00 ± 00 ± 054 ± 170 ± 054 ± 90 ± 00 ± 0
pointmaze-teleport-stitch44 ± 747 ± 240 ± 748 ± 345 ± 466 ± 327 ± 12 ± 410 ± 530 ± 3
Average3150463745793558430
Table 2. Generalization on visual antmaze stitching datasets. Success rate (%).
visual antmazeAE-GCFBC+ MC-Aug+ TD-Aug2+ TD-AugGCBCGCIQLQRLCRLHIQL
visual-antmaze-medium-stitch45 ± 460 ± 256 ± 184 ± 769 ± 49 ± 00 ± 082 ± 292 ± 1
visual-antmaze-large-stitch12 ± 119 ± 19 ± 028 ± 121 ± 61 ± 01 ± 029 ± 646 ± 2
Average2940335645515669
Table 3. Manipulation with oracle goals and action chunking. Success rate (%).
EnvironmentGCFBC+ TD-Aug2+ TD-AugGCIQLHIQL
playstitchstitchstitchstitchstitch
cube-double75 ± 120 ± 078 ± 284 ± 063 ± 16 ± 2
cube-triple35 ± 520 ± 036 ± 531 ± 28 ± 20 ± 0
puzzle-4x423 ± 20 ± 018 ± 040 ± 216 ± 50 ± 0
Average44134452292

Mean ± standard deviation over 3 seeds, after averaging the last 3 checkpoints within each seed. TD-Aug2 uses TD2-β; TD-Aug uses MCHC-β. Bold highlights the best BC augmentation and the best method overall on stitching datasets.