# Lambda-Hold Control: Human-Like Movement Emerges from a Minimal Task Reward in Predictive Musculoskeletal Simulation

arXiv: https://arxiv.org/abs/2608.17030 · HTML: https://mlsanity.com/paper/2608.17030/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 17 of its 71 references that are in the map.
- First posted on arXiv 17 Aug 2026.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 17 of 17)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [The Option-Critic Architecture](https://mlsanity.com/paper/1609.05140/) (2016)
- [Maximum a Posteriori Policy Optimisation](https://mlsanity.com/paper/1806.06920/) (2018)
- [First return, then explore](https://mlsanity.com/paper/2004.12919/) (2020)
- [Emergence of Locomotion Behaviours in Rich Environments](https://mlsanity.com/paper/1707.02286/) (2017)
- [MyoSuite -- A contact-rich simulation suite for musculoskeletal motor control](https://mlsanity.com/paper/2205.13600/) (2022)
- [Learning Symmetric and Low-energy Locomotion](https://mlsanity.com/paper/1801.08093/) (2018)
- [When Waiting is not an Option : Learning Options with a Deliberation Cost](https://mlsanity.com/paper/1709.04571/) (2017)
- [Smooth Exploration for Robotic Reinforcement Learning](https://mlsanity.com/paper/2005.05719/) (2020)
- [Learning to Repeat: Fine Grained Action Repetition for Deep Reinforcement Learning](https://mlsanity.com/paper/1702.06054/) (2017)
- [DEP-RL: Embodied Exploration for Reinforcement Learning in Overactuated and Musculoskeletal Systems](https://mlsanity.com/paper/2206.00484/) (2022)
- [Latent Exploration for Reinforcement Learning](https://mlsanity.com/paper/2305.20065/) (2023)
- [SAR: Generalization of Physiological Agility and Dexterity via Synergistic Action Representation](https://mlsanity.com/paper/2307.03716/) (2023)
- [A novel plasticity rule can explain the development of sensorimotor intelligence](https://mlsanity.com/paper/1505.00835/) (2015)
- [Muscle Synergy Priors Enhance Biomechanical Fidelity in Predictive Musculoskeletal Locomotion Simulation](https://mlsanity.com/paper/2603.10474/) (2026)

## Abstract (arXiv)

The massive overactuation in the human musculoskeletal system makes it challenging to train musculoskeletal models to generate human-like motion via reinforcement learning, primarily because exploration in the resulting high-dimensional and redundant action space is extremely inefficient. To address this problem, we propose the λ-hold controller, inspired by the equilibrium-point (EP) hypothesis, which has been widely supported by extensive evidence from human motor control studies. The policy's control variable is the per-muscle EP threshold length λ, from which a stretch-reflex recruitment law computes the muscle excitations automatically. Holding each λ over an interval of the gait phase also sharply reduces the frequency at which the policy must be queried. Consequently, the controller, to our knowledge for the first time, enables a muscle-actuated skeletal model to learn human-like sprinting using only a minimal reward within an hour of training. The efficient exploration through the proposed λ-hold controller is not merely an engineering trick but an approach grounded in physiology, bringing together the EP hypothesis, intermittent control, and optimal feedback control. Beyond encapsulating human-like behavior in predictive simulation, this achievement contributes to developing a learnable model of the human motor controller.