Reinforcement Learning with Verifiable Reward (RLVR) has significantly advanced the complex reasoning abilities of Large Language Models (LLMs). However, it struggles to break through the inherent capability boundaries of the base LLM, due to its essentially on-policy strategy coupled with LLM’s immense action space and sparse reward. Critically, RLVR can lead to the capability boundary collapse, narrowing the LLM’s problem-solving scope. To address this problem, we propose R-PLUS, a novel hybrid-policy optimization approach for LLMs that synergizes internal exploitation with external data to achieve stronger reasoning capabilities and surpass the boundaries of base models. R-PLUS integrates two core components, i.e., Multiple Importance Sampling to address distributional mismatch from external data, and Exploration-Based Advantage Function to guide the model towards high-value, unexplored reasoning paths. We provide both theoretical analysis and extensive experiments to demonstrate the superiority and generalizability of our approach. Compared with existing RLVR methods, R-PLUS achieves 1) state-of-the-art performance on six math reasoning benchmarks; 2) superior performance on six out-of-distribution reasoning tasks; 3) consistent and significant gains across diverse model families, with average relative improvements up to 69.2%. Moreover, the analysis of Pass@k curves indicates that R-PLUS effectively resolves the capability boundary collapse problem.

While Large Language Models (LLMs) excel at code generation by learning from vast code corpora, a fundamental semantic gap remains between their training on textual patterns and the goal of functional correctness, which is governed by formal execution semantics. Reinforcement Learning with Verifiable Rewards (RLVR) approaches attempt to bridge this gap using outcome rewards from executing test cases. However, solely relying on binary pass/fail signals is inefficient for establishing a well-aligned connection between the textual representation of code and its execution semantics, especially for subtle logical errors within the code. In this paper, we propose CODERL+, a novel approach that integrates execution semantics alignment into the RLVR training pipeline for code generation. CODERL+ enables the model to infer variable-level execution trajectory, providing a direct learning signal of execution semantics. CODERL+ can construct execution semantics alignment directly using existing on-policy rollouts and integrates seamlessly with various RL algorithms. Extensive experiments demonstrate that CODERL+ outperforms post-training baselines (including RLVR and Distillation), achieving a 4.6% average relative improvement in pass@1. CODERL+ generalizes effectively to other coding tasks, yielding 15.5% and 4.4% higher accuracy on code-reasoning and test-output-generation benchmarks, respectively. CODERL+ shows strong applicability across diverse RL algorithms and LLMs. Furthermore, probe analyses provide compelling evidence that CODERL+ strengthens the alignment between code’s textual representations and its underlying execution semantics.