arXiv:2606.15301v1 Announce Type: cross Abstract: The Lenstra-Lenstra-Lov\'asz (LLL) algorithm is a seminal contribution to computer science used for lattice basis reduction, yet its polynomial-time outputs produce bases that are far from optimal as the dimension grows. We show that deep reinforcement learning can discover strictly superior, generalizable reduction strategies by interacting with the primitive action space of LLL. We formulate lattice reduction as a single-player Markov Decision Process (MDP) and train a deep residual network using an AlphaZero-style self-play pipeline augmente
The rapid advancements in deep reinforcement learning and self-play algorithms, particularly inspired by systems like AlphaZero, are enabling new breakthroughs in complex optimization problems previously considered intractable or limited by heuristic approaches.
This development indicates a significant shift in how foundational computational problems, like lattice reduction which underpins cryptography and coding theory, can be optimized, potentially leading to more efficient and secure systems.
Traditional heuristic-based algorithms for lattice reduction can now be augmented or surpassed by AI-discovered strategies, improving efficiency and potentially opening new avenues in computational mathematics and security.
- · AI/ML researchers
- · Cryptography
- · High-performance computing
- · Data security
- · Traditional optimization algorithm developers
More efficient lattice reduction algorithms will enhance the performance of lattice-based cryptography and other computational tasks.
Improved cryptographic methods could provide stronger data security and resilience against certain types of attacks.
The success here may inspire AI-driven exploration and optimization of other foundational mathematical algorithms, accelerating scientific discovery across various domains.
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Read at arXiv cs.AI