ShardNet: Training Neural Controllers with Hard, Non-Convex Constraints

2026-06-29

AI Summary

This work addresses the challenge of enforcing strict, non-convex hard safety constraints in safety-critical systems, where existing neural network controllers often treat safety as a competing objective and lack formal guarantees. The paper proposes ShardNet, a novel architecture that embeds safety mechanisms directly into the network structure by jointly parameterizing a differentiable projection layer with a classifier. This approach enables, for the first time, constructive synthesis of controllers that provably satisfy safety constraints defined by non-convex polyhedra or sublevel sets of learned value functions in closed-loop systems. The method supports correct training of ReLU-based value functions and verification of forward-invariant safe sets. Evaluated on a double-integrator benchmark, ShardNet achieves 100% verified safety with significantly lower task loss than existing formal methods and generates safe sets over three times larger than those produced by current approaches.

Abstract

While neural network control policies are powerful, their deployment on safety critical systems depends on ensuring that they obey strict constraints. Existing work often treats safety as a metric to optimize for, which competes with other performance objectives, if training converges at all. Instead, we introduce ShardNet, a neural network architecture that strictly enforces unions of polyhedral constraints by construction, using a differentiable projection layer parameterized by a classification network. The key insight is to embed safety into the neural network's structure, allowing performance to be optimized independently because formal safety guarantees are always given. In contrast with existing neural architectures that can only enforce simple convex constraints, ShardNet enables the first safe-by-construction synthesis of forward-invariant neural network controllers on closed-loop systems where safety constraints are expressed as nonconvex unions of polyhedras or learned value function level sets. To support this, we also introduce a technique to verify and train such value functions correctly as rectified linear unit (ReLU) networks, which has not previously been possible. On double integrator benchmarks drawn from the literature, ShardNet policies maintain 100% safety on verified sets and achieves significantly lower objective loss compared to existing formal methods. Furthermore, our value function training technique also produces safe sets more than 3 times larger than existing verification approaches.

Problem

• neural network control
• non-convex constraints
• safety guarantees
• forward invariance
• formal verification

Innovation

• ShardNet
• non-convex constraints
• safe-by-construction
• differentiable projection
• ReLU value function verification