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Handling Long and Richly Constrained Tasks through Constrained Hierarchical Reinforcement Learning
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Proposes CoSHRL, a hierarchical RL method pairing a goal-conditioned distributional RL low-level agent with a ConstrainedRRT* upper-level search that enforces expected or CVaR cost constraints over long-horizon navigation without retraining.
Problem
Long-horizon goal-directed RL with trajectory-level safety constraints, including percentile (CVaR) cost constraints, where existing constrained RL methods only handle short horizons and need retraining when thresholds change.
Approach
Combine an upper-level Informed RRT*-based search that builds waypoints under CVaR cost constraints (checked by convolving segment cost distributions) with a lower-level goal-conditioned distributional RL agent that estimates local reward and cost distributions, so cost thresholds can change without retraining.
Key results
- CoSHRL achieves about 100% success rate in the obstacle-only point maze, outperforming SORB with a growing margin as difficulty increases.
- In the static-hazard maze, CoSHRL reaches the goal with nearly 100% success while SAC-Lagrangian and WCSAC achieve near 0% success on this long-horizon task; GRL succeeds under 20%.
- In Safe-ViZDoom, CoSHRL achieves over 95% success with cost-limit violations of only 2%, 4%, 5% for K=0,4,8, while unconstrained SORB and GRL exceed cost 8 in over half of trajectories.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CoSHRL with risk level α=0.1 instead of α=0.9 | CoSHRL · Stochastic-cost point maze | trajectories exceeding cost limit: 16% -> 7% | Helped |
| Use CoSHRL with risk level α=0.1 instead of α=0.9 | CoSHRL · Stochastic-cost point maze | expected negated reward (ENR): 47.83 -> 48.60 | Helped |
| Use CoSHRL with risk level α=0.1 instead of α=0.9 | CoSHRL · Stochastic-cost point maze | expected cost (EC): 7.90 -> 6.47 | Helped |
| Use CoSHRL with risk level α=0.1 instead of α=0.9 | CoSHRL · Stochastic-cost point maze | cost-CVaR-0.1: 14.67 -> 12.11 | Hurt |
| Use CoSHRL with risk level α=0.9 instead of SORB | Stochastic-cost point maze · Stochastic-cost point maze | expected negated reward (ENR): 52.98 -> 47.83 | Helped |
| Use CoSHRL with risk level α=0.9 instead of SORB | Stochastic-cost point maze · Stochastic-cost point maze | cost-CVaR-0.9: 8.97 -> 8.47 | Helped |
Surprising findings
- WCSAC and SAC-Lagrangian achieve roughly 0% success on the long-horizon hazard maze task.
- CoSHRL slightly violates the CVaR bound at the tight level alpha=0.1 due to discretization and truncation in distributional RL.
Limitations
- Assumes the low-level agent reliably reaches each waypoint; poor generalization can declare reachable states unreachable, yielding no path (success rate not exactly 100%).
- Cost estimates degrade as paths traverse more hazardous area, and CVaR constraint is slightly violated at tight alpha.
- Asymptotic optimality proof relies on robustly optimal solution assumptions and a theoretical framework from prior RRT* analysis.
Experimental setup
Datasets: point maze environments Safe-ViZDoom
Benchmarks: 2D point maze navigation with obstacles 2D point maze with hazards (static and stochastic cost) Safe-ViZDoom image navigation
Metrics: success rate negated reward (path length) cost violation proportion CVaR of cost expected cost
Baselines: SAC-Lagrangian WCSAC SORB Goal-conditioned RL (GRL)
Builds on: Informed RRT* RRT* SORB goal-conditioned RL distributional RL
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