So Paulo State Universiy
Abstract
Binary systems host complex orbital dynamics where test particles can occupy
stable regions despite strong gravitational perturbations. The sailboat region,
discovered in the Pluto-Charon system, allows highly eccentric S-type orbits at
intermediate distances between the two massive bodies. This region challenges
traditional stability concepts by supporting eccentricities up to 0.9 in a zone
typically dominated by chaotic motion. We investigate the sailboat region's
existence and extent across different binary system configurations. We examine
how variations in mass ratio, secondary body eccentricity, particle
inclination, and argument of pericenter affect this stable region. We performed
1.2 million numerical simulations of the elliptic three-body problem to
generate four datasets exploring different parameter spaces. We trained XGBoost
machine learning models to classify stability across approximately $10^9$
initial conditions. We validated our results using Poincar\'e surface of
section and Lyapunov exponent analysis to confirm the dynamical mechanisms
underlying the stability. The sailboat region exists only for binary mass
ratios $\mu = [0.05, 0.22]$. Secondary body eccentricity severely constrains
the region, following an exponential decay: $e_{s,\mathrm{max}} \approx 0.016 +
0.614 \exp(-25.6\mu)$. The region tolerates particle inclinations up to
$90^\circ$ and persists in retrograde configurations for $\mu \leq 0.16$.
Stability requires specific argument of pericenter values within $\pm 10^\circ$
to $\pm 30^\circ$ of $\omega = 0^\circ$ and $180^\circ$. Our machine learning
models achieved over 97\% accuracy in predicting stability. The sailboat region
shows strong sensitivity to system parameters, particularly secondary body
eccentricity. Among Solar System dwarf planet binaries, Pluto-Charon,
Orcus-Vanth and Varda-Ilmar\"e systems could harbor such regions.
AI Insights - XGBoost models trained on 1.2 million three‑body integrations classify ~10⁹ initial conditions with >97 % accuracy.
- The sailboat region exists only for mass ratios μ∈[0.05,0.22], shrinking toward the primary as μ increases.
- Secondary eccentricity limits the region exponentially: e_s,max≈0.016+0.614 exp(−25.6μ).
- Stability persists for inclinations up to 90°, including retrograde orbits when μ≤0.16.
- The argument of pericenter must lie within ±10°–30° of 0° or 180° for the sailboat region to survive.
- Poincaré surfaces of section and Lyapunov exponents confirm the dynamical mechanisms behind the stable zone.
- The ML pipeline can cut simulation time by up to 10⁵×, enabling rapid surveys of binary system stability.
Beihang University, China
Abstract
In cooperative Multi-Agent Reinforcement Learning (MARL), it is a common
practice to tune hyperparameters in ideal simulated environments to maximize
cooperative performance. However, policies tuned for cooperation often fail to
maintain robustness and resilience under real-world uncertainties. Building
trustworthy MARL systems requires a deep understanding of robustness, which
ensures stability under uncertainties, and resilience, the ability to recover
from disruptions--a concept extensively studied in control systems but largely
overlooked in MARL. In this paper, we present a large-scale empirical study
comprising over 82,620 experiments to evaluate cooperation, robustness, and
resilience in MARL across 4 real-world environments, 13 uncertainty types, and
15 hyperparameters. Our key findings are: (1) Under mild uncertainty,
optimizing cooperation improves robustness and resilience, but this link
weakens as perturbations intensify. Robustness and resilience also varies by
algorithm and uncertainty type. (2) Robustness and resilience do not generalize
across uncertainty modalities or agent scopes: policies robust to action noise
for all agents may fail under observation noise on a single agent. (3)
Hyperparameter tuning is critical for trustworthy MARL: surprisingly, standard
practices like parameter sharing, GAE, and PopArt can hurt robustness, while
early stopping, high critic learning rates, and Leaky ReLU consistently help.
By optimizing hyperparameters only, we observe substantial improvement in
cooperation, robustness and resilience across all MARL backbones, with the
phenomenon also generalizing to robust MARL methods across these backbones.
Code and results available at
https://github.com/BUAA-TrustworthyMARL/adv_marl_benchmark .
AI Insights - The study documents compliance with the NeurIPS Code of Ethics, detailing safeguards for high‑risk model release.
- All data and model owners are credited with explicit license terms, ensuring reproducibility and legal integrity.
- A curated ethics resource list—books, AAAI papers, EU guidelines, NeurIPS site, Stanford Coursera—guides responsible AI research.
- Compute requirements for reproducing the 82k experiments are fully disclosed, enabling transparent benchmarking.
- No human subjects or crowdsourcing were involved, so IRB approval was unnecessary while still addressing participant risk.
- Key terms such as “NeurIPS Code of Ethics” and “LLM usage” are explicitly defined, clarifying scope for future work.
- By integrating ethics with empirical robustness analysis, the paper invites exploration of trustworthy MARL without compromising rigor.