# AlphaG-OPD: Reliability-Gated Sibling Counterfactuals for On-Policy Distillation in Symbolic Alpha Factor Discovery

arXiv: https://arxiv.org/abs/2608.01303 · HTML: https://mlsanity.com/paper/2608.01303/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 35 of its 50 references that are in the map.
- First posted on arXiv 2 Aug 2026.

## Placed in

- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [Policy Distillation](https://mlsanity.com/paper/1511.06295/) (2015)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [On-Policy Context Distillation for Language Models](https://mlsanity.com/paper/2602.12275/) (2026)
- [A Closer Look at Invalid Action Masking in Policy Gradient Algorithms](https://mlsanity.com/paper/2006.14171/) (2020)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [Better Training of GFlowNets with Local Credit and Incomplete Trajectories](https://mlsanity.com/paper/2302.01687/) (2023)
- [Qlib: An AI-oriented Quantitative Investment Platform](https://mlsanity.com/paper/2009.11189/) (2020)
- [Towards Understanding and Improving GFlowNet Training](https://mlsanity.com/paper/2305.07170/) (2023)
- [HIST: A Graph-based Framework for Stock Trend Forecasting via Mining Concept-Oriented Shared Information](https://mlsanity.com/paper/2110.13716/) (2021)
- [AlphaAgent: LLM-Driven Alpha Mining with Regularized Exploration to Counteract Alpha Decay](https://mlsanity.com/paper/2502.16789/) (2025)
- [Asymmetric On-Policy Distillation: Bridging Exploitation and Imitation at the Token Level](https://mlsanity.com/paper/2605.06387/) (2026)
- [AlphaEvolve: A Learning Framework to Discover Novel Alphas in Quantitative Investment](https://mlsanity.com/paper/2103.16196/) (2021)
- [Filter, Then Reweight: Rethinking Optimization Granularity in On-Policy Distillation](https://mlsanity.com/paper/2606.02684/) (2026)
- [REST: Relational Event-driven Stock Trend Forecasting](https://mlsanity.com/paper/2102.07372/) (2021)
- [AlphaForge: A Framework to Mine and Dynamically Combine Formulaic Alpha Factors](https://mlsanity.com/paper/2406.18394/) (2024)
- [Prune-OPD: Efficient and Reliable On-Policy Distillation for Long-Horizon Reasoning](https://mlsanity.com/paper/2605.07804/) (2026)
- [Unmasking On-Policy Distillation: Where It Helps, Where It Hurts, and Why](https://mlsanity.com/paper/2605.10889/) (2026)
- [Decoupling KL and Trajectories: A Unified Perspective for SFT, DAgger, Offline RL, and OPD in LLM Distillation](https://mlsanity.com/paper/2605.16826/) (2026)
- [Prefix Teach, Suffix Fade: Local Teachability Collapse in Strong-to-Weak On-Policy Distillation](https://mlsanity.com/paper/2605.13643/) (2026)

## Abstract (arXiv)

Symbolic alpha factor discovery can score a completed expression, but it provides no direct label for the structural decisions that produced it. Generative flow networks (GFlowNets) preserve a diverse, reward-proportional distribution over complete expressions, yet their trajectory-level objective does not compare unchosen sibling actions at an intermediate state. We introduce AlphaG-OPD, a structural on-policy distillation framework that turns terminal factor evaluations into local action guidance. Its design separates three decisions. Component I determines where to teach by exposing grammar-valid siblings at partial abstract-syntax-tree (AST) states visited by the current forward policy. Component II determines what is reliable enough to teach: it evaluates three supported siblings under four shared suffixes and admits a KL-bounded target only when their matched comparisons exhibit sufficient winner agreement and a positive empirical lower confidence bound (LCB). Component III determines how strongly and for how long to teach by consolidating accepted targets through bounded replay, score-indexed expiry, and forward-gradient balancing, without additional factor evaluations. Terminal reward, Trajectory Balance, the backward policy, grammar, and factor-pool rules remain unchanged. An equal-physical-score four-arm ablation tests paired teaching, reliability gating, and consolidation. Across China's CSI300, CSI500, and CSI1000 and the U.S. S&P 500, the complete method delivers strong cross-market performance over multiple random seeds.