# Successive Convex Approximation Based Off-Policy Optimization for Constrained Reinforcement Learning

arXiv: https://arxiv.org/abs/2105.12545 · HTML: https://mlsanity.com/paper/2105.12545/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 33 references that are in the map.
- First posted on arXiv 26 May 2021.

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

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Learning Dexterous In-Hand Manipulation](https://mlsanity.com/paper/1808.00177/) (2018)
- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [Responsive Safety in Reinforcement Learning by PID Lagrangian Methods](https://mlsanity.com/paper/2007.03964/) (2020)
- [Safe Exploration in Continuous Action Spaces](https://mlsanity.com/paper/1801.08757/) (2018)
- [Projection-Based Constrained Policy Optimization](https://mlsanity.com/paper/2010.03152/) (2020)
- [A Tour of Reinforcement Learning: The View from Continuous Control](https://mlsanity.com/paper/1806.09460/) (2018)
- [Lyapunov-based Safe Policy Optimization for Continuous Control](https://mlsanity.com/paper/1901.10031/) (2019)
- [Provably Efficient Safe Exploration via Primal-Dual Policy Optimization](https://mlsanity.com/paper/2003.00534/) (2020)
- [Finite-Sample Analysis for SARSA with Linear Function Approximation](https://mlsanity.com/paper/1902.02234/) (2019)
- [Convergent Policy Optimization for Safe Reinforcement Learning](https://mlsanity.com/paper/1910.12156/) (2019)
- [P3O: Policy-on Policy-off Policy Optimization](https://mlsanity.com/paper/1905.01756/) (2019)
- [Constrained Markov Decision Processes via Backward Value Functions](https://mlsanity.com/paper/2008.11811/) (2020)
- [Artificial Intelligence-Enabled Intelligent 6G Networks](https://mlsanity.com/paper/1912.05744/) (2019)
- [Randomized Channel Sparsifying Hybrid Precoding for FDD Massive MIMO Systems](https://mlsanity.com/paper/1906.01516/) (2019)

## Built on by (most cited first, 5 of 5)

- [Asynchronous Multi-Model Dynamic Federated Learning over Wireless Networks: Theory, Modeling, and Optimization](https://mlsanity.com/paper/2305.13503/) (2023)
- [A Hybrid Reinforcement Learning Framework for Hard Latency Constrained Resource Scheduling](https://mlsanity.com/paper/2504.03721/) (2025)
- [A Single-Loop Deep Actor-Critic Algorithm for Constrained Reinforcement Learning with Provable Convergence](https://mlsanity.com/paper/2306.06402/) (2023)
- [Context-aware Constrained Reinforcement Learning Based Energy-Efficient Power Scheduling for Non-stationary XR Data Traffic](https://mlsanity.com/paper/2503.09391/) (2025)
- [Joint User Priority and Power Scheduling for QoS-Aware WMMSE Precoding: A Constrained-Actor Attentive-Critic Approach](https://mlsanity.com/paper/2506.16074/) (2025)

## Abstract (arXiv)

We propose a successive convex approximation based off-policy optimization (SCAOPO) algorithm to solve the general constrained reinforcement learning problem, which is formulated as a constrained Markov decision process (CMDP) in the context of average cost. The SCAOPO is based on solving a sequence of convex objective/feasibility optimization problems obtained by replacing the objective and constraint functions in the original problems with convex surrogate functions. At each iteration, the convex surrogate problem can be efficiently solved by Lagrange dual method even the policy is parameterized by a high-dimensional function. Moreover, the SCAOPO enables to reuse old experiences from previous updates, thereby significantly reducing the implementation cost when deployed in the real-world engineering systems that need to online learn the environment. In spite of the time-varying state distribution and the stochastic bias incurred by the off-policy learning, the SCAOPO with a feasible initial point can still provably converge to a Karush-Kuhn-Tucker (KKT) point of the original problem almost surely.