humancompatible.interconnect is an open-source toolkit for the modelling, simulations, and theorem proving within ergodicity of multi-agent systems.
Notably, the toolkit makes it possible to test contraction-on-average (sufficient and sometimes necessary) conditions for unique ergodicity via stochastic approximation, i.e., to check if unique invariant measure exists. This is a prerequisite for most definitions of fairness in repeated uses of AI systems. The toolkit also makes it possible to estimate this unique invariant measure, if it does exist.
- Approximation of the modulus of local Lipschitz continuity on average for an iterated function system:
from tests.contractionTests.contraction_test import get_factor_from_list
C = get_factor_from_list(reference_signals=reference_signals,
agent_probs=np.array([[eps, 1-eps], [eps, 1-eps]]),
sim_class=Sim,
it=100,
trials=20,
weights="./weights/weights_basic_ReLU.pth",
node_outputs_plot="A1",
show_distributions_plot=True,
show_distributions_histograms_plot=False)- Approximating the unique invariant measure of the system:
from humancompatible.interconnect.simulators.distribution import *
reference_signals = np.array([4, 5, 20, 25])
fig, ax = plt.subplots()
outputs = generate_outputs(sim_class=Sim,
weights="./weights/weights_basic_ReLU.pth",
reference_signals=reference_signals,
node="A1",
iterations=100,
samples=100)
distributions = get_distributions(x=outputs,
h=1.9,
labels=[f"reference_signal = {r}" for r in reference_signals],
step=0.1,
node="A1",
show_plots=True,
show_histograms=True,
fig=fig,
ax=ax)examples/basic_simulation_ReLU - example notebook featuring the calls above.
Other example notebooks can be found in the same folder.
For more background, see our AAMAS tutorial (https://humancompatible.org/index.php/2024/05/05/fairness-in-the-sharing-economy-and-stochastic-models-for-mas/), or the original papers:
arXiv:1807.03256 (https://arxiv.org/abs/1807.03256) On the Ergodic Control of Ensembles Andre R. Fioravanti, Jakub Marecek, Robert N. Shorten, Matheus Souza, Fabian R. Wirth Comments: Journal version of Fioravanti et al. [arXiv:1703.07308, CDC 2017] Journal-ref: Automatica, Volume 108, October 2019
arXiv:2007.16117 (https://arxiv.org/abs/2007.16117) Predictability and Fairness in Social Sensing Ramen Ghosh, Jakub Marecek, Wynita M. Griggs, Matheus Souza, Robert N. Shorten Journal-ref: IEEE Internet of Things Journal, 2021
arXiv:2110.03001 (https://arxiv.org/abs/2110.03001) Predictability and Fairness in Load Aggregation and Operations of Virtual Power Plants Jakub Marecek, Michal Roubalik, Ramen Ghosh, Robert N. Shorten, Fabian R. Wirth Journal-ref: Automatica, Volume 147, January 2023, 110743
arXiv:2112.06767 (https://arxiv.org/abs/2112.06767) On the Ergodic Control of Ensembles in the Presence of Non-linear Filters Vyacheslav Kungurtsev, Jakub Marecek, Ramen Ghosh, Robert N. Shorten Journal-ref: Automatica, Volume 152, June 2023, 110946
arXiv:2104.14858 (https://arxiv.org/abs/2104.14858) Unique Ergodicity in the Interconnections of Ensembles with Applications to Two-Sided Markets Wynita M. Griggs, Ramen Ghosh, Jakub Marecek, Robert N. Shorten
arXiv:2209.01410 (https://arxiv.org/abs/2209.01410) Closed-Loop View of the Regulation of AI: Equal Impact across Repeated Interactions Quan Zhou, Ramen Ghosh, Robert Shorten, Jakub Marecek
The illustrative notebooks draw upon the code developed for the papers above by:
Wynita Griggs Michal Roubalik Matheus Souza Quan Zhou