Learning Robot Policies from Sparse Success Signals via STL-Guided Stein Variational Policy Gradient

Signal Temporal Logic (STL) enables formal specification of complex spatiotemporal constraints for robotic task planning. However, synthesizing long-horizon continuous control trajectories from complex STL specifications is fundamentally challenging due to the nested structure of STL robustness objectives. Existing solver-based methods, such as Mixed-Integer Linear Programming (MILP), suffer from exponential scaling, whereas sampling methods, such as Model-Predictive Path Integral control (MPPI), struggle with sparse, long-horizon costs. We introduce Signal Temporal Logic guided Stein Variational Path Integral Optimization (STL-SVPIO), which reframes STL as a globally informative, differentiable reward-shaping mechanism. By leveraging Stein Variational Gradient Descent and differentiable physics engines, STL-SVPIO transports a mutually repulsive swarm of control particles toward high robustness regions. Our method transforms sparse logical satisfaction into tractable variational inference, mitigating the severe local minima traps of standard gradient-based methods. We demonstrate that STL-SVPIO significantly outperforms existing methods in both robustness and efficiency for traditional STL tasks. Moreover, it solves complex long-horizon tasks, including multi-agent coordination with synchronization and queuing while baselines either fail to discover feasible solutions, or become computationally intractable. Finally, we use STL-SVPIO in agile robotic motion planning tasks with nonlinear dynamics, such as 7-DoF manipulation and half cheetah back flips to show the generalizability of our algorithm.

Video-based policy learning is particularly promising, as it illustrates target behaviors without requiring action annotations or embodiment-matched demonstrations. A central challenge is deciding what information should be transferred from the video to the robot. Existing approaches commonly convert visual observations into scalar similarity or value signals, or ask foundation models to directly generate reward code. These approaches can make the temporal structure of a task difficult to inspect, ground, and reuse. We present Video2STL, a framework that converts observation-only videos into parametric Signal Temporal Logic (STL) specifications and uses the resulting formal representation for robot learning. A vision-language model extracts an embodiment-independent semantic event trace and constructs a bank of symbolic temporal specifications. The model determines the task structure, while numerical predicate thresholds and temporal bounds are grounded from successful robot trajectories. For policy learning, we separate short- and long-timescale temporal information: short-horizon specifications provide dense rewards through rolling-window quantitative robustness, while a causal monitor over a retained long-horizon specification provides one-time progress rewards for valid temporal prefixes. The same representation supports cross-embodiment transfer from human or animal videos to robot control. Across four manipulation tasks, Video2STL achieves $85.8\%$ average success-once and $67.0\%$ success-at-end, compared with $81.5\%/59.5\%$ for native dense PPO and $65.0\%/42.3\%$ for Text2Reward; in quadruped locomotion, Qwen-3.8 and GPT-5.6-based Video2STL policies achieve $100\%$ success across velocities from $0.3$ to $2.1\,\mathrm{m/s}$ while remaining competitive in high-speed energy efficiency. Project webpage: video2stl.

Reinforcement learning (RL) for quadruped locomotion commonly depends on fixed, hand-crafted, and Markovian reward functions that limit both interpretability of learned policies and lack explicit control over gait behaviors. We introduce a framework where distinct gaits are specified using parameterized constraints expressed in Signal Temporal Logic (STL). These include safety bounds, gait synchronization constraints, command tracking, and actuation bounds. From these specifications, we develop a reward shaping mechanism that provides learning agents a dense, continuous reward landscape that encodes desired behavior. We define parametric STL templates for three speed regimes (walking-trot, trot, bound), calibrate their parameters from reference rollouts, and compute rewards from using smooth approximations of STL robustness over the rollouts. The generated rewards can be used to provide shaped gradients compatible with Proximal Policy Optimization (PPO). We instantiate the approach on Google's Barkour quadruped robot in MuJoCo XLA (MJX). We use parallelization within the simulator to improve training speeds and use domain randomization to robustify learned policies. We show that compared to a baseline of hand-crafted rewards, the STL-shaped rewards yield tighter velocity tracking and more stable training. Videos can be found on our project website: https://stl-locomotion.github.io/.