Graph-Aware Exploration Strategies

• Graph-aware exploration is a paradigm that uses adaptive environment graphs to modulate agent learning through dynamic terrain configuration and feedback-driven adjustments.
• It employs both procedural methods and LLM-based generation to systematically vary environment complexity, promoting skill acquisition and sample efficiency.
• Implementations like TerrainRLSim, GenEnv, and EnvGen demonstrate significant improvements in learning outcomes via iterative curriculum alignment and difficulty calibration.

Graph-aware exploration encompasses adaptive environment generation and parameterization methodologies that modulate agent learning by controlling the structure, challenge, and composition of the interaction space ("level environment"). Central to this paradigm is the automated construction and feedback-driven adaptation of environment graphs—typically expressed as configuration vectors or generative policies—that expose agents to an evolving spectrum of state transitions and objective landscapes. Modern instantiations leverage LLMs both as agents and meta-environment designers, orchestrating environment difficulty, diversity, and morphology to maximize skill acquisition, sample efficiency, and generalization. The canonical formulations are exemplified in frameworks such as TerrainRLSim (Berseth et al., 2018), GenEnv (Guo et al., 22 Dec 2025), and EnvGen (Zala et al., 2024), which formalize exploration via explicit parameter families and iterative curriculum alignment.

1. Formulation of Level Environments and Terrain Graphs

Level environments (frequently abbreviated as LevelEnv) are parameterized as configuration vectors or terrain files that fully specify the transition graph within simulation episodes. In the Terrain RL Simulator (Berseth et al., 2018), each LevelEnv instance consists of a terrain generator $G$ governed by a parameter vector $$\theta = (\mathit{GapSpacing}, \mathit{GapWidth}, \mathit{StepHeight}, \dots)$$, where each component is sampled independently (i.i.d.) from prescribed ranges: $$\theta_i \sim \mathrm{Uniform}( \mathrm{min}_i, \mathrm{max}_i )$$ The joint density over terrain configurations is then $$p(\theta) = \prod_i 1/(\mathrm{max}_i - \mathrm{min}_i)$$. This procedural mechanism constructs dynamic terrain graphs composed of segments (gaps, slopes, walls) that challenge agent locomotion policies.

In LLM-driven frameworks (EnvGen, GenEnv), the environment is a $d$-dimensional vector $E \in \mathbb{R}^d$ controlling terrain mixture weights, resource spawn rates, and initialization, with the LLM serving as a graph designer—iteratively outputting novel $E$ based on agent feedback (Zala et al., 2024): $$\{ E^{(t)}_i \}_{i=1}^N \approx \arg\max_{E_1,\dots,E_N} \sum_{i=1}^N R_{\mathrm{gen}}^{(t)}(E_i)$$ where $R_{\mathrm{gen}}^{(t)}(E)$ measures expected learning progress on weak objectives.

2. Difficulty Calibration and Curriculum Alignment

Environment difficulty is not absolute but contingent on both agent morphology and the expansiveness of the environment graph. In TerrainRLSim, difficulty is empirically correlated with:

• Action space dimensionality $d_A$
• Spread of terrain parameters (wider range $[\mathrm{min}, \mathrm{max}]$ implies higher obstacle variance)
• Obstacle types (flat $\rightarrow$ incline $\rightarrow$ steps $\rightarrow$ gaps $\rightarrow$ mixed $\rightarrow$ dynamic)

This calibration enables a graded suite of 89 environments, supporting systematic exploration and transfer across agent morphologies and actuation models (Berseth et al., 2018). Difficulty feedback is operationalized via agent learning curves, e.g., time-to-threshold reward or success rate evolution.

In GenEnv, environment difficulty is dynamically aligned to the agent’s "zone of proximal development" using the $\alpha$-Curriculum Reward (Guo et al., 22 Dec 2025): $$\hat{p} = \frac{k}{n} , \qquad R_{\mathrm{env}}(\hat{p}) = \exp( -\beta ( \hat{p} - \alpha )^2 )$$ where $k$ successes out of $n$ tasks define $\hat{p}$, and $\alpha$ (usually 0.5) aligns tasks to be neither trivial nor intractable. The policy $\pi_{\mathrm{env}}$ adapts its generative output to maintain $\hat{p}$ within a target threshold window.

3. Feedback-Driven Environment Generation Loop

The core mechanic in graph-aware exploration is a closed feedback loop wherein agent performance informs subsequent environment graph instantiation. In EnvGen, this takes the form of an iterative cycle:

• Agent trains in LLM-generated environments, yielding success rates $P_j^{(t)}$ per objective $o_j$
• Agent feedback (success percentages) is verbatim inserted into the LLM prompt
• The LLM outputs batches of $N$ new environments $E^{(t)}_i$ focusing on weakest skills (Zala et al., 2024)
• Optimal improvement is implicitly rewarded via: $$R_{\mathrm{gen}}^{(t)}(E) = \sum_{j=1}^M (1-P_j^{(t-1)}) \, [P_j^{(t)}(E) - P_j^{(t-1)}]$$ Environments thus adapt to "fill gaps" in the agent's performance, guiding exploration toward underskilled regions of the state graph.

4. Implementation Architectures and APIs

TerrainRLSim exposes a Gym-style API interfacing with Bullet Physics at up to 3 kHz, with JSON terrain files and Python hooks for direct parameter manipulation (Berseth et al., 2018). Morphology, actuation, and environment type are encoded in the environment name string, enabling on-the-fly changes:

• env = terrainRLSim.getEnv(env_name="PD_Biped3D_SlopesMixed-v0")
• tg = env.terrain_generator
• tg.setParam("GapSpacingMin", 1.5)

LLM-based generation (EnvGen, GenEnv) employs prompt engineering and seed context, inserting performance feedback and difficulty control constraints directly in the prompt (Guo et al., 22 Dec 2025, Zala et al., 2024). The environment generator and policy are typically instantiated from the same base LLM checkpoint (e.g., Qwen2.5-7B-Instruct), using optimization methods such as Reward-Weighted Regression (RWR) and GRPO.

5. Empirical Results, Ablation Studies, and Optimization Granularity

Ablation studies in EnvGen highlight the necessity of feedback-driven adaptation:

• Fixed environments yield lower scores versus adaptive updates (e.g., Crafter: 29.9% vs 32.2%)
• Granularity matters: optimal at 4 cycles $\times$ 4 environments, diminishing returns with more frequent updates
• LLM model quality is critical (GPT-4-Turbo outperforms smaller LLMs)
• Balanced training in LLM-generated and original environments maximizes generalization (Zala et al., 2024)

GenEnv’s co-evolutionary curriculum achieves significant performance improvements—ALFWorld rises from 14.2% to 54.5% (+40.3%), BFCL from 7.0% to 41.8% (+34.8%)—while maintaining data efficiency (outperforming Gemini 2.5 Pro offline approaches using 3.3$\times$ less data) (Guo et al., 22 Dec 2025).

6. Practical Roles and Future Directions

Graph-aware exploration frameworks enable fine-grained control over agent learning by shaping the transition graph with parameterized morphology, obstacle type, and adaptive curriculum. They are well-suited for domains requiring sample efficiency, targeted skill acquisition, and progressive difficulty ramping. Future directions may investigate richer rule-based, probabilistic, or noise-correlated terrain graphs, deeper LLM prompt engineering for environment synthesis, and formalization of environment-agent mutual information as a difficulty signal. A plausible implication is the extension to continual learning regimes, where environment graphs perpetually evolve to probe model robustness across unseen and adversarial transitions.