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IEEE Congress on Information Science and Technology (CiSt)

Hyperparameter Optimization and Neuroevolution with Binary Quadratic Meta-heuristics and Evolution Strategies

David Von Dollen, Reuben Brasher, Florian Neukart, Thomas Bäck

Published Dec 16, 2023• 2 citations
Publisher

Abstract

This study extends previous work on quantum-enhanced selection operators [Von Dollen et al.(2022)], where selection operators of evolutionary algorithms for classical black-box optimization are framed as quadratic binary optimization (QUBO) models, applied to black-box objective functions. We test our algorithms using both elitist and non-elitist strategies. First, we benchmark all heuristics over black-box, multi-modal functions. We find that for 94.4% of test cases, our method shows performance improvements with respect to fitness. Then, we similarly benchmark over the problem of hyperparameter selection for machine learning models, also a black-box optimization problem, and compare it to random search. We find that our method achieves some improvement with an average validation accuracy of 98.492% and highest ranking of 4.529412 (out of 5) when averaged across all test cases. We also apply our method towards neuroevolution, where we evolve weight spaces for small feedforward neural networks for learning tasks. In these settings, our method shows improved average reward in the reinforcement learning case and increased velocity in learning the XOR function.

DOI
10.1109/cist56084.2023.10409984

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This study extends previous work on quantum-enhanced selection operators [Von Dollen et al.(2022)], where selection operators of evolutionary algorithms for classical black-box optimization are framed as quadratic binary optimization (QUBO) models, applied to black-box objective functions. We test our algorithms using both elitist and non-elitist strategies. First, we benchmark all heuristics over black-box, multi-modal functions. We find that for 94.4% of test cases, our method shows performance improvements with respect to fitness. Then, we similarly benchmark over the problem of hyperparameter selection for machine learning models, also a black-box optimization problem, and compare it to random search. We find that our method achieves some improvement with an average validation accuracy of 98.492% and highest ranking of 4.529412 (out of 5) when averaged across all test cases. We also apply our method towards neuroevolution, where we evolve weight spaces for small feedforward neural networks for learning tasks. In these settings, our method shows improved average reward in the reinforcement learning case and increased velocity in learning the XOR function.
Neuroevolution, a field that draws inspiration from the evolution of brains in nature, harnesses evolutionary algorithms to construct artificial neural networks. It bears a number of intriguing capabilities that are typically inaccessible to gradient-based approaches, including optimizing neural-network architectures, hyperparameters, and even learning the training rules. In this paper, we introduce a quantum neuroevolution algorithm that autonomously finds near-optimal quantum neural networks for different machine-learning tasks. In particular, we establish a one-to-one mapping between quantum circuits and directed graphs, and reduce the problem of finding the appropriate gate sequences to a task of searching suitable paths in the corresponding graph as a Markovian process. We benchmark the effectiveness of the introduced algorithm through concrete examples including classifications of real-life images and symmetry-protected topological states. Our results showcase the vast potential of neuroevolution algorithms in quantum architecture search, which would boost the exploration towards quantum-learning advantage with noisy intermediate-scale quantum devices.
Abstract As restricted quantum computers become available, research focuses on finding meaningful applications. For example, in quantum machine learning, a special type of quantum circuit called a quantum neural network is one of the most investigated approaches. However, we know little about suitable circuit architectures or important model hyperparameters for a given task. In this work, we apply the functional ANOVA framework to the quantum neural network architectures to analyze which of the quantum machine learning hyperparameters are most influential for their predictive performance. We restrict our study to 7 open-source datasets from the OpenML-CC18 classification benchmark, which are small enough for simulations on quantum hardware with fewer than 20 qubits. Using this framework, three main levels of importance were identified, confirming expected patterns and revealing new insights. For instance, the learning rate is identified as the most important hyperparameter on all datasets, whereas the particular choice of entangling gates used is found to be the least important on all except for one dataset. In addition to identifying the relevant hyperparameters, for each of them, we also learned data-driven priors based on values that perform well on previously seen datasets, which can then be used to steer hyperparameter optimization processes. We utilize these priors in the hyperparameter optimization method hyperband and show that these improve performance against uniform sampling across all datasets by, on average, 0.53%0.53 \%0.53% 0.53 % , up to 6.11%6.11 \%6.11% 6.11 % , in cross-validation accuracy. We also demonstrate that such improvements hold on average regardless of the configuration hyperband is run with. Our work introduces new methodologies for studying quantum machine learning models toward quantum model selection in practice. All research code is made publicly available.
Quantum computing combined with machine learning, is a promising emerging field for tackling problems that are extremely expensive or fundamentally infeasible for classical computers. Nonetheless, design of the optimal quantum circuit for machine learning is a major challenge, which can be attributed to the exponential search space of the quantum gate arrangement and unmatched structured design methods. To resolve this, our work introduces a novel automated framework for quantum architecture search (AQAS) that adopts both meta-learning and evolutionary algorithms to automatically learn, transfer, and optimize quantum circuit architectures to suit different machine learning tasks. Our strategy relies on meta-learning to introduce a learning scheme, i.e. it allows the AQAS system to generalize across distributions by learning from a shared structural and functional prior from the distribution of machine learning problems. This enables the approach to quickly home in effective quantum circuit implementations for new tasks with low data or retraining. At the same time, we use evolutionary algorithms– mimicking natural selection– to breed populations of quantum circuit architectures. These circuits are represented in genotypes, are varied under mutation and crossover, and are selected according to a fitness function that blends quantum resource utilization (e.g., depth, qubits) with task-specific performance (e.g., classification accuracy or loss). The architecture is realized in a mixed quantum-classical environment, with quantum circuits simulated on quantum simulators and/or Noisy-Intermediate-Scale-Quantum (NISQ) devices. We verify the effectiveness of our approach on a number of benchmarked datasets and tasks which range from quantum-aided image recognition, time series prediction to medical diagnostics. We demonstrate that AQAS can discover compact, high-performing quantum models, which generalize better and are computationally more efficient than the custom-built quantum models.
We introduce a variational quantum algorithm to solve unconstrained black box binary optimization problems, i.e., problems in which the objective function is given as black box. This is in contrast to the typical setting of quantum algorithms for optimization where a classical objective function is provided as a given Quadratic Unconstrained Binary Optimization problem and mapped to a sum of Pauli operators. Furthermore, we provide theoretical justification for our method based on convergence guarantees of quantum imaginary time evolution.To investigate the performance of our algorithm and its potential advantages, we tackle a challenging real-world optimization problem: feature selection . This refers to the problem of selecting a subset of relevant features to use for constructing a predictive model such as fraud detection. Optimal feature selection---when formulated in terms of a generic loss function---offers little structure on which to build classical heuristics, thus resulting primarily in ‘greedy methods’. This leaves room for (near-term) quantum algorithms to be competitive to classical state-of-the-art approaches. We apply our quantum-optimization-based feature selection algorithm, termed VarQFS, to build a predictive model for a credit risk data set with 20 and 59 input features (qubits) and train the model using quantum hardware and tensor-network-based numerical simulations, respectively. We show that the quantum method produces competitive and in certain aspects even better performance compared to traditional feature selection techniques used in today's industry.
Abstract Variational quantum algorithms, a class of quantum heuristics, are promising candidates for the demonstration of useful quantum computation. Finding the best way to amplify the performance of these methods on hardware is an important task. Here, we evaluate the optimization of quantum heuristics with an existing class of techniques called “meta-learners.” We compare the performance of a meta-learner to evolutionary strategies, L-BFGS-B and Nelder-Mead approaches, for two quantum heuristics (quantum alternating operator ansatz and variational quantum eigensolver), on three problems, in three simulation environments. We show that the meta-learner comes near to the global optima more frequently than all other optimizers we tested in a noisy parameter setting environment. We also find that the meta-learner is generally more resistant to noise, for example, seeing a smaller reduction in performance inNoisyandSamplingenvironments, and performs better on average by a “gain” metric than its closest comparable competitor L-BFGS-B. Finally, we present evidence that indicates the meta-learner trained on small problems will generalize to larger problems. These results are an important indication that meta-learning and associated machine learning methods will be integral to the useful application of noisy near-term quantum computers.
Quantum hardware and quantum-inspired algorithms are becoming increasingly popular for combinatorial optimization. However, these algorithms may require careful hyperparameter tuning for each problem instance. We use a reinforcement learning agent in conjunction with a quantum-inspired algorithm to solve the Ising energy minimization problem, which is equivalent to the Maximum Cut problem. The agent controls the algorithm by tuning one of its parameters with the goal of improving recently seen solutions. We propose a new Rescaled Ranked Reward (R3) method that enables a stable single-player version of self-play training and helps the agent escape local optima. The training on any problem instance can be accelerated by applying transfer learning from an agent trained on randomly generated problems. Our approach allows sampling high quality solutions to the Ising problem with high probability and outperforms both baseline heuristics and a black-box hyperparameter optimization approach.