MA-WAMMulti-Agent World-Action Model for Test-Time Planning

Main results against published baselines

Main results across MPE, SMAC, and MA-MuJoCo. Entries are episode returns; MPE uses the normalized score scale, whereas SMAC and MA-MuJoCo use native returns. MA-WAM (ours) reports mean ± standard deviation across seeds, while published baselines retain their source-paper uncertainty conventions. Baseline abbreviations follow the manuscript.

MPE

SMAC

MA-MuJoCo

Planning versus direct execution

Per-setting planning gain with three denoising steps per candidate. Reported scores are means under the common evaluation protocol; MPE uses normalized score, while SMAC and MA-MuJoCo use raw return. Δ is Planning minus Reactive, computed before display rounding, and bold marks a positive Δ. Planning improves the mean on 26 of 30 settings.

Aggregate gains by benchmark

Benchmark-level seed-averaged gain summary with three denoising steps per candidate. Mean Δ is in each benchmark's native unit. Aggregate relative gain is computed after summing reactive and planning scores within each benchmark family. Mean and median setting-wise gains first compute a relative gain for each task--quality setting and then aggregate those percentages within the benchmark family.

Equal-budget ablation: RWM versus random selection

Full 30-setting equal-candidate selector control with three denoising steps per candidate. Each entry is a mean under the common evaluation protocol. Both arms use M=8 candidates; Random selects uniformly, whereas RWM ranks candidates by predicted return. MPE uses OMAR normalized score; SMAC and MA-MuJoCo use native returns. Within each block, Δ is RWM minus Random, computed before display rounding; bold marks a positive difference. RWM exceeds Random in mean on 23 settings.

Same-state candidate-ranking reliability

Same-state counterfactual candidate-ranking diagnostic on MPE and MAMuJoCo Medium tasks using 64 anchor states per task. RWM is compared with the analytical chance references for Top-1, Top-2, and Spearman rank correlation, and with the 0.5 chance reference for PairAcc (pairwise ranking accuracy). NormReg (normalized selection regret) compares RWM selection with empirical uniform selection from the same candidate sets.

Inference cost across candidate budgets

Candidate-count profiling on an RTX 3090 and an A100. Results are averaged equally over MPE Spread-Medium, MAMuJoCo 2Ant-Medium, and SMAC 3m-Medium. Candidates are generated sequentially and scored in one batched RWM pass. We use four parallel environments, K=3, and a requested rollout cap H=8; the effective action horizons are 8/8/3 in the listed task order. Each entry is the mean of three repeats, each with 10 warm-up and 30 timed steps per setting. Total is Gen. plus Score.

Batched versus sequential generation

Batched versus sequential candidate-generation latency for six Medium settings at M=8. We use the protocol of the corresponding table in the paper: four parallel environments, K=3, a requested rollout cap of eight, and three repeats with 10 warm-up and 30 timed steps per setting. Batch folds the M candidates into one generation pass; ``×'' is the within-row generation speedup. Times are milliseconds. ``Qual.'' is the number of task--quality settings sharing that architecture. The effective horizon for SMAC 3m is three. The A100 measurements were taken on a shared node.

SMAC success rates

SMAC win rate; higher is better. Reactive uses M=1, whereas planning uses M=8 under the horizon protocol in Appendix (paper). Both use the fixed three-step denoising budget of the corresponding table in the paper. Planning improves 8 of 12 settings and ties 2 at the win-rate floor. Δ is Planning minus Reactive, and bold marks an improvement.