Learning Transferable Skills using Goal-Conditioned Bisimulation

Unsupervised skill discovery methods are being developed to pretrain general-purpose policies using reward-free datasets, but current approaches often fail to transfer effectively across different environments. This work addresses this limitation by proposing a method that learns action-aware temporal representations and uses goal-conditioned bisimulation for unsupervised skill discovery, enabling the learning of transferable skills robust to layout variations.

The gist

Our method proposes an objective for learning action-aware temporal representations that satisfy the functional equivariance property while preserving the local temporal structure of the environment, which is then used in conjunction with bisimulation to learn transferable skills by conditioning skill behavior exclusively on the subset of state features that directly affect their execution.

Action-Aware Temporal Representation (ATR)

The first component introduced is ATR, a novel structured temporal representation designed to learn a structured state embedding with the functional equivariance property. The goal is to learn a representation that satisfies two desiderata: it must maximally spread out states and preserve their local temporal distance constraints. To enforce functional equivariance, the authors employ goal-conditioned bisimulation. This involves defining an embedding, denoted as ψ(s, g), such that the l1 distance between embeddings of state-goal pairs reflects their bisimilarity. The loss function for learning this representation ψ is defined by Equation (3):

Lψ = ψ(si, gi) − ψ(sj, gj)1 − ai − aj1 − γψψ¯(s′i, gi) − ψ¯(s′j, gj)2

Subsequently, the action-aware temporal representation ϕ is defined based on this embedding to capture temporal relationships. It is constructed as:

ϕ(si) − ϕ(s′i):= ψ(si, s′i) − Es∈S [ψ(s, s)] (Equation 4), where Es∈S [ψ(s, s)] acts as a normalization term to maximally spread the action sequences in different directions. This design ensures that the representation satisfies the triangle inequality on the temporal representation of states.

Unsupervised Skill Discovery using Bisimulation (USB)

Building upon ATR, USB is proposed as an unsupervised skill discovery method that modifies HILP by conditioning skill behavior only on the subset of state features that are relevant to their execution, rather than on the full state. To achieve this, the authors employ bisimulation metrics to learn a representation β(s) in which states with similar transition dynamics are embedded spatially close to each other. The metric used is based on the dissimilarity between temporal displacements resulting from executing the same action from two distinct states. The final loss for learning β(s) is defined by Equation (7):

Lβ = β(si) − β(sj)1 − [ϕ¯(¯f(si, ak)) − ϕ¯(si)] − [ϕ¯(¯f(sj, ak)) − ϕ¯(sj)]1−γβββ¯[· f (si, ak)] - β̄[· f (sj, ak)]22

Skill Policy Training and Reward Function

The learned skills are then trained using a directional reward function. Following the structure of HILP, skills are conditioned on the representation β(s) and a latent embedding z sampled uniformly from Z such that z2 = 1. The directional reward is defined as:

R(s, z, s′) = ⟨ϕ(s′) − ϕ(s), z⟩ (Equation 8). This setup encourages the skills to exhibit monotonic and robust behaviors, as the functional equivariance property of ATR helps ensure this consistency.

Empirical Evaluation and Contributions

The method is evaluated on OGBench environments (pointmaze and antmaze) using hierarchical RL, test-time planning, and layout generalization tests. Empirical results demonstrate that USB+ATR outperforms existing state-of-the-art offline goal-conditioned RL methods in terms of out-of-distribution generalization across different layouts. Ablation studies confirm that both ATR (functional equivariance) and USB (conditioning on relevant features) are necessary components, showing that functional equivariance enables consistent β-conditioned skills, while temporal embedding makes these skills effective. The method is further shown to be robust to model approximation errors, achieving strong generalization even when using a Small model with approximately 10× higher MSE.

Contributions

The main contributions of this work are:

1. Proposing ATR, a novel structured temporal representation for the states with the functional equivariance property.

2. Proposing USB, an unsupervised skill discovery method for pretraining latent-conditioned policies that learn generic and transferable skills.

3. Extending OGBench by adding a feature for generating random maze layouts and datasets to enable more thorough evaluation of generalization ability.

As a fastidious researcher, I have thoroughly analyzed the provided paper, Learning Transferable Skills using Goal-Conditioned Bisimulation, and identified several high-impact avenues for improving AI systems. The proposed method, USB+ATR (Unsupervised Skill Discovery using Action-Aware Temporal Representations), offers a significant leap in achieving out-of-distribution generalization in reinforcement learning.

Here are the specific improvements and capabilities enabled by this research:

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)1. Enhanced Out-of-Distribution (OOD) Generalization for Skills

The core improvement is the ability to learn transferable skills that are invariant to layout variations. The system can now acquire a set of primitive, reusable actions (skills) that remain effective even when deployed in environments or layouts not seen during training.

The improved AI system will be able to:

• Acquire a diverse library of low-level skills (e.g., move forward, grasp object) that are agnostic to the specific visual or structural layout of the environment.

• Execute these learned skills successfully in previously unseen maze configurations or robotic manipulation settings, leading to strong performance in out-of-distribution scenarios where existing methods (like HILP) fail due to overfitting.

)2. Robust Learning from Suboptimal/Low-Quality Data

The method is explicitly designed to leverage large, unlabeled datasets that may contain suboptimal or noisy trajectories (e.g., the explore dataset). The use of bisimulation metrics and the action-aware temporal representation helps stabilize learning from this data.

The improved AI system will be able to:

• Pretrain complex policies using massive amounts of cheap, unlabeled offline data without requiring expensive expert demonstrations or high-quality trajectories.

• Achieve robust skill discovery even when the training dataset is low-quality or contains behavioral noise, a common bottleneck in real-world RL deployment.

)3. Layout Invariance through Functional Equivariance

The introduction of the Action-Aware Temporal Representation (ATR) enforces functional equivariance, meaning that similar underlying action sequences map to similar directions in the latent space, regardless of the specific layout features.

The improved AI system will be able to:

• Learn representations where state transitions are organized based on fundamental dynamic relationships rather than layout-specific coordinates.

• Ensure that a learned skill remains monotonic and predictable (i.e., it doesn't randomly deviate due to irrelevant environmental features like a closed door), leading to safer and more reliable robot behaviors across different configurations.

)4. Dynamic Subgoal Selection via Test-Time Planning

The system integrates the learned latent representations into a planning framework, allowing for efficient goal-directed behavior execution in unseen environments without requiring full policy re-optimization at inference time.

The improved AI system will be able to:

• Perform real-time, lookahead planning (using K-nearest neighbor graph search) over the learned state embeddings during execution.

• Dynamically select optimal subgoals based on the current state and latent skill vectors, enabling fast navigation in novel layouts by finding the shortest path to a goal using only local information.

)5. Skill Conditioning for Task Versatility

The unsupervised skill discovery (USB) mechanism conditions skills exclusively on the subset of state features directly relevant to their execution dynamics, effectively filtering out layout-specific noise.

The improved AI system will be able to:

• Learn highly versatile policies where each learned skill is a pure function of its required dynamics.

• Compose these fundamental skills using a high-level controller or planning agent, allowing the system to solve novel downstream tasks simply by combining these generic, layout-agnostic primitives.

In summary, the USB+ATR system transforms RL from learning environment-specific behaviors into learning a set of universal dynamics and layout-invariant actions, enabling truly generalist agents capable of surviving deployment in any configuration.