Skip to content

tsallis_mppi_reproduction.md

Latest commit

 

History

History
167 lines (131 loc) · 8.06 KB

tsallis_mppi_reproduction.md

File metadata and controls

167 lines (131 loc) · 8.06 KB
Raw

Tsallis-MPPI Lightweight Reproduction

Target

The paper generalizes VI-MPC, MPPI, CEM, and SVGD-style MPC under a Tsallis divergence objective. The practical control hook is replacing the usual exponential optimality likelihood with a deformed, q-exponential transform, which changes how aggressively high-cost samples are downweighted.

Implemented Scope

This repository now has a lightweight nav reproduction in src/benchmark_diff_mppi.cu:

  • use_tsallis_weights, tsallis_q, tsallis_temperature, and tsallis_min_weight in PlannerVariant.
  • compute_tsallis_weights_kernel, which applies a normalized q-exponential transform to rollout costs and renormalizes the sample weights.
  • Three planner variants:
    • tsallis_mppi_q07: compact-support style q-exponential with q=0.70.
    • tsallis_mppi_smooth: q=0.70 plus the existing low-pass update (low_pass_alpha=0.20).
    • tsallis_mppi_q13: heavy-tail style q-exponential with q=1.30.

The implementation intentionally keeps the existing CUDA MPPI rollout path and only swaps the sample likelihood/weight transform. It does not reproduce the full VI-MPC derivation, mixture policy update, covariance update, warm-up optimization loop, or stochastic dynamics ensemble from the paper.

The q-exponential used here is:

exp_q(x) = [1 + (1 - q) x]_+ ^ (1 / (1 - q))

with the standard exponential as the q -> 1 fallback. Costs are normalized against the rollout minimum before the transform for stability.

Build And Benchmark

Build:

cmake --build build-docker-smoke --target benchmark_diff_mppi -j$(nproc)

Benchmark:

./bin/benchmark_diff_mppi --quick \
    --scenarios dynamic_bottleneck,dynamic_pincer,dynamic_crossing,uncertain_crossing \
    --planners mppi,lp_mppi_smooth,tsallis_mppi_q07,tsallis_mppi_smooth,tsallis_mppi_q13,step_mppi_smooth,csc_mppi_smooth,dm_mppi_smooth \
    --k-values 32,64,128 \
    --seed-count 3 \
    --csv build-docker-smoke/tsallis_mppi_compare.csv && \
    python3 scripts/summarize_diff_mppi.py \
      --csv build-docker-smoke/tsallis_mppi_compare.csv \
      --markdown-out build-docker-smoke/tsallis_mppi_compare_summary.md \
      --time-caps 0.25,0.5,1.0 \
      --time-targets 0.25,0.5

Artifacts:

  • build-docker-smoke/tsallis_mppi_compare.csv
  • build-docker-smoke/tsallis_mppi_compare_summary.md
  • build-docker-smoke/tsallis_mppi_compare_summary.tex

All table values below are means over 3 seeds.

Strong Positive Result: Cheap Dynamic Bottleneck Fix

tsallis_mppi_smooth solves the narrow timing-gate case where vanilla MPPI, LP-MPPI, and Step-MPPI stall. It is much cheaper and smoother than CSC/DM, but less robust at K=64.

Scenario K Planner Success Steps Final Dist Cum. Cost Avg Control ms Roughness Collisions
dynamic_bottleneck 32 mppi 0.00 320.0 24.52 46936.6 0.13 1.86 0.00
dynamic_bottleneck 32 lp_mppi_smooth 0.00 320.0 24.55 46444.6 0.14 0.49 0.00
dynamic_bottleneck 32 step_mppi_smooth 0.00 320.0 24.43 46390.8 0.14 0.60 0.00
dynamic_bottleneck 32 tsallis_mppi_q07 0.00 320.0 24.95 46769.0 0.13 2.36 0.00
dynamic_bottleneck 32 tsallis_mppi_smooth 1.00 287.3 1.91 36381.3 0.13 0.50 0.00
dynamic_bottleneck 32 csc_mppi_smooth 1.00 272.0 1.90 34622.3 0.68 2.50 0.00
dynamic_bottleneck 32 dm_mppi_smooth 1.00 279.3 1.94 35585.1 0.91 3.32 0.00
dynamic_bottleneck 64 tsallis_mppi_smooth 0.67 305.7 9.69 40647.1 0.14 0.27 0.00
dynamic_bottleneck 128 tsallis_mppi_smooth 1.00 307.0 1.89 38885.6 0.16 0.16 0.00

Interpretation: q-reweighted samples plus low-pass smoothing suppress the weighted-average stall without adding the expensive representative selection used by CSC or the influence scan used by DM.

Positive Result: Open Dynamic Crossings

In open crossing scenes, tsallis_mppi_smooth is competitive with LP/Step and keeps the same lightweight runtime envelope.

Scenario K Planner Success Steps Final Dist Cum. Cost Avg Control ms Roughness
dynamic_crossing 128 mppi 0.00 260.0 3.20 46034.9 0.16 0.60
dynamic_crossing 128 lp_mppi_smooth 1.00 252.7 1.89 41670.5 0.18 0.11
dynamic_crossing 128 step_mppi_smooth 1.00 251.0 1.93 41218.1 0.15 0.13
dynamic_crossing 128 tsallis_mppi_q07 1.00 250.7 1.93 41033.5 0.18 0.50
dynamic_crossing 128 tsallis_mppi_smooth 1.00 249.3 1.96 40780.6 0.18 0.17
dynamic_crossing 128 csc_mppi_smooth 1.00 249.7 1.93 41010.2 1.40 3.09
dynamic_crossing 128 dm_mppi_smooth 1.00 250.0 1.88 40961.7 2.55 3.58
uncertain_crossing 128 tsallis_mppi_smooth 1.00 250.0 1.92 40919.4 0.15 0.15

Partial Result: Dynamic Pincer

The pincer scene is not the main win. tsallis_mppi_smooth reaches full success at K=64 and K=128, but LP is already strong in this benchmark pass.

Scenario K Planner Success Steps Final Dist Cum. Cost Avg Control ms Roughness
dynamic_pincer 64 mppi 0.00 260.0 9.67 47889.6 0.16 1.16
dynamic_pincer 64 lp_mppi_smooth 1.00 257.3 1.95 42238.8 0.16 0.23
dynamic_pincer 64 step_mppi_smooth 0.33 258.7 2.04 42049.4 0.20 0.26
dynamic_pincer 64 tsallis_mppi_q07 0.33 260.0 2.04 41739.4 0.18 0.96
dynamic_pincer 64 tsallis_mppi_smooth 1.00 259.0 1.95 41796.7 0.18 0.31
dynamic_pincer 64 tsallis_mppi_q13 0.00 260.0 2.86 43708.8 0.18 0.88
dynamic_pincer 128 tsallis_mppi_smooth 1.00 259.0 1.91 41695.1 0.17 0.15

Negative Result: q Shape Matters

The q setting is not a cosmetic parameter:

  • tsallis_mppi_q07 without low-pass over-prunes the useful sample set and stalls in the bottleneck at all tested rollout counts.
  • tsallis_mppi_q13 keeps too much heavy-tail mass in the bottleneck and collides frequently: average collisions were 11.33, 34.33, and 8.00 at K=32, K=64, and K=128.
  • tsallis_mppi_smooth is the only useful variant from this pass; the low-pass update is part of the working recipe, not a presentation tweak.

Fixed-Time Summary

Under the 0.25 ms wall-clock cap, tsallis_mppi_smooth is the only tested planner with aggregate success 1.00 across the four stress scenarios:

Cap ms Planner Success Steps Final Dist Cum. Cost Avg Control ms Mean K
0.25 mppi 0.17 269.4 6.39 45021.0 0.16 96
0.25 lp_mppi_smooth 0.75 270.4 7.58 42941.0 0.15 56
0.25 step_mppi_smooth 0.75 270.1 7.54 42734.2 0.18 72
0.25 tsallis_mppi_q07 0.58 270.5 7.66 42614.5 0.18 128
0.25 tsallis_mppi_q13 0.50 273.1 7.28 57504.0 0.14 72
0.25 tsallis_mppi_smooth 1.00 267.0 1.90 40649.3 0.15 88

Takeaways

  • Keep tsallis_mppi_smooth as a low-cost timing-gate stabilizer.
  • Do not use unsmoothed q=0.70 for bottlenecks; it gets stuck.
  • Do not use q=1.30 in constrained dynamic scenes without an additional safety layer; its heavy-tail behavior caused collisions in the bottleneck.
  • CSC/DM remain more principled robust planners for hard bottlenecks, but they are much more expensive in this reproduction.
  • The next useful step is combining Tsallis weighting with the existing Shield/BC safety filters to see whether the low-cost bottleneck gain survives with explicit collision suppression.