# Stanford Robotics Seminar ENGR319 | Autumn 2026 | Bridging Rigorous Methods with Machine Learning

## Executive summary

This seminar proposes a comprehensive framework for building safe and intelligent autonomous systems by synthesizing rigorous, model-based methods with scalable, data-driven machine learning. The approach is divided into two complementary paths: ensuring safety and mission satisfaction by design (using hard constraints) and generating evidence of failure through advanced, adaptive testing. Key technical advancements include using Control Barrier Functions (CBFs) to embed safety guarantees directly into reinforcement learning policies, and employing probabilistic sampling techniques (like MCMC) and Active Inference to efficiently discover complex failure modes in black-box systems.

## Key takeaways

- Bridging Rigor and Data-Driven Methods: Classical methods offer strong, provable safety guarantees but struggle with scalability and model complexity. Pure data-driven approaches (ML/RL) are scalable and model-free but often rely on empirical, rather than rigorous, guarantees. The goal is to combine the strengths of both into a single framework.
- Safety by Design: Hard Constraints: Safety constraints must be enforced as hard constraints, not soft penalties. This is achieved by formulating the safety requirements as a Control Barrier Function (CBF) or Graph Control Barrier Function (GCBF). These functions provide a mathematically rigorous guarantee that a safe action exists, even in multi-agent, partially observable systems.
- Mission Specification via Temporal Logic: Complex, infinite-horizon mission goals (e.g., 'must revisit location A, then B') can be precisely described using Temporal Logic, a systematic symbolic language. This allows the mission objective to be decomposed into solvable, atomic value functions.
- Adaptive Failure Discovery (Active Inference): Instead of assuming a clear cost function (J) for failure, the system treats failure discovery as an inference process. An adaptive framework actively and sequentially generates the 'most informative test cases' by optimizing for information gain and user utility, moving from limited evidence to deployable evidence.

## Technical details

- Control Barrier Functions (CBF): A CBF is a function that takes the system state and outputs a scalar value, indicating whether the state is safe (positive) or unsafe (negative). For multi-agent systems, a Graph CBF (GCBF) allows each agent to use only local observations while maintaining a global safety guarantee for the entire system.
- Temporal Logic: A systematic symbolic language used to describe complex, infinite-horizon mission requirements (e.g., 'always avoid the wall' or 'eventually reach goal B'). The ability to decompose these tasks into fundamental, solvable value functions is key to scalable policy learning.
- Failure Modeling and Sampling: Failure testing is reframed from a difficult optimization problem (finding the exogenous parameters Y that maximize cost J) to a probabilistic sampling problem. This uses Markov Chain Monte Carlo (MCMC) sampling from a posterior distribution to efficiently locate high-cost failure regions.
- Active Inference: This adaptive framework guides test case generation by maximizing two metrics: Information Gain (reducing uncertainty about failure) and User Utility (addressing subjective failure criteria). This allows the system to learn from limited evidence (simulators, historical failures) to generate robust, deployable test cases.

## Practical implications

- Developing highly reliable autonomous systems (e.g., warehouse logistics, multi-drone coordination) that can operate safely at scale.
- Improving the robustness of self-driving algorithms by enforcing complex traffic rules as hard constraints.
- Evaluating the trustworthiness of Large Language Models (LLMs) by generating stress-test scenarios (e.g., pre/post-disaster satellite images) to identify failure modes and low confidence outputs.
- Creating standardized, mathematically guaranteed safety certificates for complex robotic deployments.

## Topics

Autonomous Systems, Control Theory, Reinforcement Learning, Formal Methods, Temporal Logic, Active Learning, System Verification, Stanford Online, Stanford ASL Robotics Seminar Archive

Source: https://www.youtube.com/watch?v=ot_whQ3xyJQ