Sairaj Dhople

Sachin Khoja, Kamlesh Sawant, Palak Jain et al.

This paper presents an automated software toolchain for synthesizing hardware-implementable analog circuits that solve constrained optimization problems. The proposed toolchain supports nonlinear objective functions with linear and quadratic constraints. It maps optimization variables to capacitor voltages, implementing dynamics that enforce Karush-Kuhn-Tucker conditions using operational amplifiers, resistors, capacitors, diodes, and analog multipliers. From high-level problem descriptions in AMPL or MPS, the toolchain generates a SPICE netlist for the analog circuit, simulates it, and verifies that the solutions converge. The projected settling time of the analog circuit depends on circuit parameters, gain-bandwidth product, and slew-rate limits of operational amplifiers, and leverages the inherent parallelism of analog circuits. The proposed toolchain successfully generates circuits with up to 10,000 variables and demonstrates large scalability improvements, achieving up to a 1,000X increase in solvable problem size over prior analog hardware demonstrations. Simulation studies further show that the automatically synthesized circuits converge to optimal solutions, achieving more than a 200X speedup compared to IPOPT, a state-of-the-art digital interior-point solver.

Xinwei Zhang, Mingyi Hong, Sairaj Dhople et al.

Federated Learning (FL) has become a popular paradigm for learning from distributed data. To effectively utilize data at different devices without moving them to the cloud, algorithms such as the Federated Averaging (FedAvg) have adopted a "computation then aggregation" (CTA) model, in which multiple local updates are performed using local data, before sending the local models to the cloud for aggregation. However, these schemes typically require strong assumptions, such as the local data are identically independent distributed (i.i.d), or the size of the local gradients are bounded. In this paper, we first explicitly characterize the behavior of the FedAvg algorithm, and show that without strong and unrealistic assumptions on the problem structure, the algorithm can behave erratically for non-convex problems (e.g., diverge to infinity). Aiming at designing FL algorithms that are provably fast and require as few assumptions as possible, we propose a new algorithm design strategy from the primal-dual optimization perspective. Our strategy yields a family of algorithms that take the same CTA model as existing algorithms, but they can deal with the non-convex objective, achieve the best possible optimization and communication complexity while being able to deal with both the full batch and mini-batch local computation models. Most importantly, the proposed algorithms are {\it communication efficient}, in the sense that the communication pattern can be adaptive to the level of heterogeneity among the local data. To the best of our knowledge, this is the first algorithmic framework for FL that achieves all the above properties.

Yu Christine Chen, Sairaj Dhople

This paper derives analytical closed-form expressions that uncover the contributions of nodal active- and reactive-power injections to the active- and reactive-power flows on transmission lines in an AC electrical network. Paying due homage to current- and voltage-divider laws that are similar in spirit, we baptize these as the power divider laws. Derived from a circuit-theoretic examination of AC power-flow expressions, the constitution of the power divider laws reflects the topology and voltage profile of the network. We demonstrate the utility of the power divider laws to the analysis of power networks by highlighting applications to transmission-network allocation, transmission-loss allocation, and identifying feasible injections while respecting line active-power flow set points.