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ESCORT: Efficient Stein-variational and Sliced Consistency-Optimized Temporal Belief Representation for POMDPs
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Proposes ESCORT, a particle-based POMDP belief representation that extends SVGD with correlation-aware sliced/projection regularization and a temporal consistency term, evaluated on POMDP domains and synthetic multi-modal distributions.
Problem
Existing POMDP belief approximators (particle filters with resampling, parametric neural/VAE beliefs, standard SVGD) fail to represent high-dimensional, multi-modal belief distributions with correlated state dimensions, leading to degraded decisions.
Approach
Extends SVGD with a correlation-aware projection regularizer (learned projection matrices, GSW-inspired) that preserves inter-dimensional dependencies, plus a temporal consistency term (sliced Wasserstein between consecutive beliefs) and a particle-based policy network trained by policy gradient.
Key results
- On 10D Light-Dark, ESCORT achieves 0.347 position error vs 0.379 for SVGD and 2.12 for POMCPOW; on 20D Kidnapped Robot it reaches 9.063 vs 10.906 for SVGD.
- In 20D synthetic distributions ESCORT attains mode coverage 1.0 while SIR drops to 0.12 and DVRL to 0.58.
- Correlation error in 20D is 0.556 for ESCORT vs 0.589 for SVGD, a modest gap at that dimension.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add correlation-aware regularization (ablation) | ESCORT · Light-Dark Navigation (10D) | position error: 0.381 $\pm$ 0.07 -> 0.347 $\pm$ 0.03 | Helped |
| add correlation-aware regularization (ablation) | ESCORT · Kidnapped Robot (20D) | position error: 10.246 $\pm$ 0.35 -> 9.063 $\pm$ 0.51 | Helped |
| add correlation-aware regularization (ablation) | ESCORT · Target Tracking (20D) | position error: 4.213 $\pm$ 0.59 -> 3.665 $\pm$ 0.31 | Helped |
| add temporal consistency regularization (ablation) | ESCORT · Light-Dark Navigation (10D) | position error: 0.321 $\pm$ 0.03 -> 0.347 $\pm$ 0.03 | Hurt |
| add temporal consistency regularization (ablation) | ESCORT · Kidnapped Robot (20D) | position error: 10.859 $\pm$ 0.51 -> 9.063 $\pm$ 0.51 | Helped |
| add temporal consistency regularization (ablation) | ESCORT · Target Tracking (20D) | position error: 3.874 $\pm$ 0.43 -> 3.665 $\pm$ 0.31 | Helped |
| use optimized rather than random projection matrices (ablation) | ESCORT · Light-Dark Navigation (10D) | position error: 0.359 $\pm$ 0.09 -> 0.347 $\pm$ 0.03 | Helped |
| use optimized rather than random projection matrices (ablation) | ESCORT · Kidnapped Robot (20D) | position error: 9.654 $\pm$ 0.32 -> 9.063 $\pm$ 0.51 | Helped |
| use optimized rather than random projection matrices (ablation) | ESCORT · Target Tracking (20D) | position error: 3.90 $\pm$ 0.42 -> 3.665 $\pm$ 0.31 | Helped |
| use ESCORT instead of SVGD | belief approximation · Synthetic 1D | Maximum Mean Discrepancy: 0.012 $\pm$ 0.01 -> 0.057 $\pm$ 0.01 | Hurt |
| use ESCORT instead of SVGD | belief approximation · Synthetic 2D | Maximum Mean Discrepancy: 0.062 $\pm$ 0.01 -> 0.052 $\pm$ 0.02 | Helped |
| use ESCORT instead of SVGD | belief approximation · Synthetic 20D | Mode Coverage: 1.0 $\pm$ 0.0 -> 1.0 $\pm$ 0.0 | No clear effect |
Surprising findings
- The no-temporal-consistency variant outperforms the full ESCORT in Light-Dark (0.321 vs 0.347).
- In 1D, standard SVGD achieves lower MMD and Wasserstein than ESCORT.
Limitations
- Computational overhead of correlation matrix and projection optimization grows with dimensionality.
- Requires known transition and observation models.
- Temporal regularization weight is domain-dependent and not clearly beneficial in all domains.
Experimental setup
Datasets: Light-Dark Navigation Kidnapped Robot Multi-Target Tracking synthetic multi-modal distributions (1D-20D)
Benchmarks: Light-Dark Navigation Kidnapped Robot Multi-Target Tracking synthetic multi-modal distributions 1D-20D
Metrics: average position error maximum mean discrepancy Wasserstein sliced Wasserstein mode coverage ratio correlation error
Baselines: SVGD DVRL POMCPOW SIR POMCP ARDESPOT AdaOPS
Builds on: Stein Variational Gradient Descent Generalized Sliced Wasserstein distance Message Passing SVGD Deep Variational Reinforcement Learning POMCPOW
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