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Optimization Algorithm Design via Electric Circuits
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Proposes designing convex optimization algorithms by building RLC circuits whose continuous-time dynamics converge to the optimum, then automatically discretizing them via performance estimation (SDP/QCQP) into provably convergent algorithms.
Problem
Designing new convex (including distributed) optimization algorithms with convergence guarantees, since classical methods have slow practice and ML optimizers lack convergence analysis.
Approach
Interpret continuous-time optimization dynamics as RLC circuits connected to the subdifferential (a nonlinear resistor), design circuits whose equilibria are primal-dual solutions, and automatically discretize them with a two-stage Runge-Kutta scheme whose parameters are found by solving a performance-estimation QCQP that certifies sufficient energy dissipation.
Key results
- DADMM+C reaches relative error 1e-10 in 66 iterations versus 87 for DADMM and 294 for P-EXTRA on a 6-node decentralized problem with 100-dimensional variables.
- Automatic discretization with PEP-based QCQP yields a provably convergent algorithm for a convex example with eta=6.66, h=6.66, alpha=0, beta=1.
- The framework recovers Nesterov acceleration, decentralized ADMM, and PG-EXTRA from RLC circuits.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add a capacitor to the DADMM circuit | DADMM · Decentralized optimization problem (6 nodes, 7 edges), relative error 10^{-10} | iterations: 87 -> 66 | Helped |
Surprising findings
- Negative resistors are needed to recover Nesterov acceleration from the circuit view, though stability is clearer via the pre-Moreau envelope.
Limitations
- Discretization relies on a non-convex QCQP solved with Ipopt, with a numerical feasibility check rather than fully exact certification.
- Analysis is limited to deterministic convex settings; stochastic setups are left to future work.
- Discretized algorithms are guaranteed to converge only for specified function classes and parameter choices found by the search.
Experimental setup
Metrics: relative error iterations to 1e-10
Baselines: DADMM P-EXTRA
Builds on: performance estimation problem Nesterov ODE decentralized ADMM PG-EXTRA
Closest papers by meaning
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- NN-Steiner: A Mixed Neural-Algorithmic Approach for the Rectilinear Steiner Minimum Tree Problem (AAAI 2024 · similarity 0.83)
- AUTOCIRCUIT-RL: Reinforcement Learning-Driven LLM for Automated Circuit Topology Generation (ICML 2025 · similarity 0.82)
- Accelerating Optimization via Differentiable Stopping Time (NeurIPS 2025 · similarity 0.82)
- Adaptive Partitioning Schemes for Optimistic Optimization (ICML 2025 · similarity 0.82)
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