# Safe Policy Optimization with Local Generalized Linear Function Approximations

arXiv: https://arxiv.org/abs/2111.04894 · HTML: https://mlsanity.com/paper/2111.04894/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 42 references that are in the map.
- First posted on arXiv 9 Nov 2021.

## Builds on (most cited first, 21 of 21)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Safe Reinforcement Learning via Shielding](https://mlsanity.com/paper/1708.08611/) (2017)
- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks](https://mlsanity.com/paper/1903.08792/) (2019)
- [Reinforcement Learning in Feature Space: Matrix Bandit, Kernels, and Regret Bound](https://mlsanity.com/paper/1905.10389/) (2019)
- [Provably Efficient Safe Exploration via Primal-Dual Policy Optimization](https://mlsanity.com/paper/2003.00534/) (2020)
- [IPO: Interior-point Policy Optimization under Constraints](https://mlsanity.com/paper/1910.09615/) (2019)
- [Safe Reinforcement Learning in Constrained Markov Decision Processes](https://mlsanity.com/paper/2008.06626/) (2020)
- [Generalization and Exploration via Randomized Value Functions](https://mlsanity.com/paper/1402.0635/) (2014)
- [Optimism in Reinforcement Learning with Generalized Linear Function Approximation](https://mlsanity.com/paper/1912.04136/) (2019)
- [Linear Stochastic Bandits Under Safety Constraints](https://mlsanity.com/paper/1908.05814/) (2019)
- [Safe Policies for Reinforcement Learning via Primal-Dual Methods](https://mlsanity.com/paper/1911.09101/) (2019)
- [Safe Exploration in Finite Markov Decision Processes with Gaussian Processes](https://mlsanity.com/paper/1606.04753/) (2016)
- [Safe Exploration for Interactive Machine Learning](https://mlsanity.com/paper/1910.13726/) (2019)
- [Constrained Markov Decision Processes via Backward Value Functions](https://mlsanity.com/paper/2008.11811/) (2020)
- [Efficient and Safe Exploration in Deterministic Markov Decision Processes with Unknown Transition Models](https://mlsanity.com/paper/1904.01068/) (2019)

## Built on by (most cited first, 10 of 10)

- [Minigrid & Miniworld: Modular & Customizable Reinforcement Learning Environments for Goal-Oriented Tasks](https://mlsanity.com/paper/2306.13831/) (2023)
- [Safe Exploration in Reinforcement Learning: A Generalized Formulation and Algorithms](https://mlsanity.com/paper/2310.03225/) (2023)
- [Generalized Linear Bandits: Almost Optimal Regret with One-Pass Update](https://mlsanity.com/paper/2507.11847/) (2025)
- [Distributionally Robust Constrained Reinforcement Learning under Strong Duality](https://mlsanity.com/paper/2406.15788/) (2024)
- [Gradient Shaping for Multi-Constraint Safe Reinforcement Learning](https://mlsanity.com/paper/2312.15127/) (2023)
- [HASARD: A Benchmark for Vision-Based Safe Reinforcement Learning in Embodied Agents](https://mlsanity.com/paper/2503.08241/) (2025)
- [Long-term Safe Reinforcement Learning with Binary Feedback](https://mlsanity.com/paper/2401.03786/) (2024)
- [Modeling Risk in Reinforcement Learning: A Literature Mapping](https://mlsanity.com/paper/2312.05231/) (2023)
- [Adaptive Aggregation for Safety-Critical Control](https://mlsanity.com/paper/2302.03586/) (2023)
- [Learning Safe Agent Behaviour from Human Preferences and Justifications via World Models](https://mlsanity.com/paper/2607.13172/) (2026)

## Abstract (arXiv)

Safe exploration is a key to applying reinforcement learning (RL) in safety-critical systems. Existing safe exploration methods guaranteed safety under the assumption of regularity, and it has been difficult to apply them to large-scale real problems. We propose a novel algorithm, SPO-LF, that optimizes an agent's policy while learning the relation between a locally available feature obtained by sensors and environmental reward/safety using generalized linear function approximations. We provide theoretical guarantees on its safety and optimality. We experimentally show that our algorithm is 1) more efficient in terms of sample complexity and computational cost and 2) more applicable to large-scale problems than previous safe RL methods with theoretical guarantees, and 3) comparably sample-efficient and safer compared with existing advanced deep RL methods with safety constraints.