MQE 0.1.5

Multistep Quasimetric Estimation - (wip)

Exploration and eventually practical implementation for the Multistep Quasimetric Estimation proposed by Zheng et al. of Berkeley.

This paper is a coming together of a few ideas: quasimetric distance spaces and successor representations, along with an action invariance loss and other loss designs

Install

pip install MQE

Usage

import torch
from torch import nn

from MQE import MQE, MRN, Policy, ContinuousAction
from x_mlps_pytorch import MLP

state_dim, action_dim = 16, 4

mrn = MRN(
    sym_network = MLP(32, 64),
    asym_network = MLP(32, 64),
    distance_groups = 8
)

mqe = MQE(
    state_encoder = MLP(state_dim, 32),
    state_action_encoder = MLP(state_dim + action_dim, 32),
    metric_residual_network = mrn
)

policy = Policy(
    action_dim = action_dim,
    dim = 32,
    state_encoder = MLP(state_dim, 32),
    goal_encoder = MLP(state_dim, 32),
    action_dist = ContinuousAction()
)

states = torch.randn(4, 10, state_dim)
actions = torch.randn(4, 10, action_dim)
goals = torch.randn(4, 10, state_dim)

# train critic from offline trajectories

critic_loss, _ = mqe(states, actions, goals)

critic_loss.backward()

# train actor using critic

policy_loss, _ = mqe.extract_policy(
    policy,
    states,
    actions,
    goals,
    bc_loss_weight = 0.1
)

policy_loss.backward()

# inference

action = policy(states[:, 0], goals[:, 0]).sample() # (4, 4)

Citations

@misc{zheng2026multistepquasimetriclearningscalable,
    title   = {Multistep Quasimetric Learning for Scalable Goal-conditioned Reinforcement Learning},
    author  = {Bill Chunyuan Zheng and Vivek Myers and Benjamin Eysenbach and Sergey Levine},
    year    = {2026},
    eprint  = {2511.07730},
    archivePrefix = {arXiv},
    primaryClass = {cs.LG},
    url     = {https://arxiv.org/abs/2511.07730},
}

@misc{liu2023metricresidualnetworkssample,
    title   = {Metric Residual Networks for Sample Efficient Goal-Conditioned Reinforcement Learning},
    author  = {Bo Liu and Yihao Feng and Qiang Liu and Peter Stone},
    year    = {2023},
    eprint  = {2208.08133},
    archivePrefix = {arXiv},
    primaryClass = {cs.LG},
    url     = {https://arxiv.org/abs/2208.08133},
}