Counterexample-driven genetic programming (CDGP) uses specifications provided as formal constraints to generate the training cases used to evaluate evolving programs. It has also been extended to combine formal constraints and user-provided training data to solve symbolic regression problems. Here we show how the ideas underlying CDGP can also be applied using only user-provided training data, without formal specifications. We demonstrate the application of this method, called ``informal CDGP,'' to software synthesis problems. Our results show that informal CDGP finds solutions faster (i.e. with fewer program executions) than standard GP. Additionally, we propose two new variants to informal CDGP, and find that one produces significantly more successful runs on about half of the tested problems. Finally, we study whether the addition of counterexample training cases to the training set is useful by comparing informal CDGP to using a static subsample of the training set, and find that the addition of counterexamples significantly improves performance.

Ensuring AI models align with human values is essential for their safety and functionality. Reinforcement learning from human feedback (RLHF) uses human preferences to achieve this alignment. However, preferences sourced from diverse populations can result in point estimates of human values that may be sub-optimal or unfair to specific groups. We propose Pareto Optimal Preference Learning (POPL), which frames discrepant group preferences as objectives with potential trade-offs, aiming for policies that are Pareto-optimal on the preference dataset. POPL utilizes Lexicase selection, an iterative process to select diverse and Pareto-optimal solutions. Our empirical evaluations demonstrate that POPL surpasses baseline methods in learning sets of reward functions, effectively catering to distinct groups without access to group numbers or membership labels. Furthermore, we illustrate that POPL can serve as a foundation for techniques optimizing specific notions of group fairness, ensuring inclusive and equitable AI model alignment.

Lexicase selection has been shown to provide advantages over other selection algorithms in several areas of evolutionary computation and machine learning. In its standard form, lexicase selection filters a population or other collection based on randomly ordered training cases that are considered one at a time. This iterated filtering process can be time-consuming, particularly in settings with large numbers of training cases. In this paper, we propose a new method that is nearly equivalent to lexicase selection in terms of the individuals that it selects, but which does so significantly more quickly. The new method, called DALex (for Diversely Aggregated Lexicase), selects the best individual with respect to a weighted sum of training case errors, where the weights are randomly sampled. This allows us to formulate the core computation required for selection as matrix multiplication instead of recursive loops of comparisons, which in turn allows us to take advantage of optimized and parallel algorithms designed for matrix multiplication for speedup. Furthermore, we show that we can interpolate between the behavior of lexicase selection and its "relaxed" variants, such as epsilon or batch lexicase selection, by adjusting a single hyperparameter, named "particularity pressure," which represents the importance granted to each individual training case. Results on program synthesis, deep learning, symbolic regression, and learning classifier systems demonstrate that DALex achieves significant speedups over lexicase selection and its relaxed variants while maintaining almost identical problem-solving performance. Under a fixed computational budget, these savings free up resources that can be directed towards increasing population size or the number of generations, enabling the potential for solving more difficult problems.

One potential drawback of using aggregated performance measurement in machine learning is that models may learn to accept higher errors on some training cases as compromises for lower errors on others, with the lower errors actually being instances of overfitting. This can lead to both stagnation at local optima and poor generalization. Lexicase selection is an uncompromising method developed in evolutionary computation, which selects models on the basis of sequences of individual training case errors instead of using aggregated metrics such as loss and accuracy. In this paper, we investigate how lexicase selection, in its general form, can be integrated into the context of deep learning to enhance generalization. We propose Gradient Lexicase Selection, an optimization framework that combines gradient descent and lexicase selection in an evolutionary fashion. Our experimental results demonstrate that the proposed method improves the generalization performance of various widely-used deep neural network architectures across three image classification benchmarks. Additionally, qualitative analysis suggests that our method assists networks in learning more diverse representations. Modern data-driven learning algorithms, in general, define an optimization objective, e.g., a fitness function for parent selection in genetic algorithms (Holland, 1992) or a loss function for gradient descent in deep learning (LeCun et al., 2015), which computes the aggregate performance on the training data to guide the optimization process. Taking the image classification problem as an example, most recent approaches use Cross-Entropy loss with gradient descent (Bottou, 2010) and backpropagation (Rumelhart et al., 1985) to train deep neural networks (DNNs) on batches of training images. Despite the success that advanced DNNs can reach human-level performance on the image recognition task (Russakovsky et al., 2015), one potential drawback for such aggregated performance measurement is that the model may learn to seek "compromises" during the learning procedure, e.g., optimizing model weights to intentionally keep some errors in order to gain higher likelihood on correct predictions.

We describe a design principle for adaptive systems under which adaptation is driven by particular challenges that the environment poses, as opposed to average or otherwise aggregated measures of performance over many challenges. We trace the development of this "particularity" approach from the use of lexicase selection in genetic programming to "particularist" approaches to other forms of machine learning and to the design of adaptive systems more generally.

Lexicase selection is a widely used parent selection algorithm in genetic programming, known for its success in various task domains such as program synthesis, symbolic regression, and machine learning. Due to its non-parametric and recursive nature, calculating the probability of each individual being selected by lexicase selection has been proven to be an NP-hard problem, which discourages deeper theoretical understanding and practical improvements to the algorithm. In this work, we introduce probabilistic lexicase selection (plexicase selection), a novel parent selection algorithm that efficiently approximates the probability distribution of lexicase selection. Our method not only demonstrates superior problem-solving capabilities as a semantic-aware selection method, but also benefits from having a probabilistic representation of the selection process for enhanced efficiency and flexibility. Experiments are conducted in two prevalent domains in genetic programming: program synthesis and symbolic regression, using standard benchmarks including PSB and SRBench. The empirical results show that plexicase selection achieves state-of-the-art problem-solving performance that is competitive to the lexicase selection, and significantly outperforms lexicase selection in computation efficiency.

In many evolutionary computation systems, parent selection methods can affect, among other things, convergence to a solution. In this paper, we present a study comparing the role of two commonly used parent selection methods in evolving machine learning pipelines in an automated machine learning system called Tree-based Pipeline Optimization Tool (TPOT). Specifically, we demonstrate, using experiments on multiple datasets, that lexicase selection leads to significantly faster convergence as compared to NSGA-II in TPOT. We also compare the exploration of parts of the search space by these selection methods using a trie data structure that contains information about the pipelines explored in a particular run.

Abstract:: NP-hard problems are not believed to be exactly solvable through general polynomial time algorithms. Hybrid quantum-classical algorithms to address such combinatorial problems have been of great interest in the past few years. Such algorithms are heuristic in nature and aim to obtain an approximate solution. Significant improvements in computational time and/or the ability to treat large problems are some of the principal promises of quantum computing in this regard. The hardware, however, is still in its infancy and the current Noisy Intermediate Scale Quantum (NISQ) computers are not able to optimize industrially relevant problems.

Lexicase selection is a semantic-aware parent selection method, which assesses individual test cases in a randomly-shuffled data stream. It has demonstrated success in multiple research areas including genetic programming, genetic algorithms, and more recently symbolic regression and deep learning. One potential drawback of lexicase selection and its variants is that the selection procedure requires evaluating training cases in a single data stream, making it difficult to handle tasks where the evaluation is computationally heavy or the dataset is large-scale, e.g., deep learning. In this work, we investigate how the weighted shuffle methods can be employed to improve the efficiency of lexicase selection. We propose a novel method, fast lexicase selection, which incorporates lexicase selection and weighted shuffle with partial evaluation. Experiments on both classic genetic programming and deep learning tasks indicate that the proposed method can significantly reduce the number of evaluation steps needed for lexicase selection to select an individual, improving its efficiency while maintaining the performance.

In genetic programming, an evolutionary method for producing computer programs that solve specified computational problems, parent selection is ordinarily based on aggregate measures of performance across an entire training set. Lexicase selection, by contrast, selects on the basis of performance on random sequences of training cases; this has been shown to enhance problem-solving power in many circumstances. Lexicase selection can also be seen as better reflecting biological evolution, by modeling sequences of challenges that organisms face over their lifetimes. Recent work has demonstrated that the advantages of lexicase selection can be amplified by down-sampling, meaning that only a random subsample of the training cases is used each generation. This can be seen as modeling the fact that individual organisms encounter only subsets of the possible environments, and that environments change over time. Here we provide the most extensive benchmarking of down-sampled lexicase selection to date, showing that its benefits hold up to increased scrutiny. The reasons that down-sampling helps, however, are not yet fully understood. Hypotheses include that down-sampling allows for more generations to be processed with the same budget of program evaluations; that the variation of training data across generations acts as a changing environment, encouraging adaptation; or that it reduces overfitting, leading to more general solutions. We systematically evaluate these hypotheses, finding evidence against all three, and instead draw the conclusion that down-sampled lexicase selection's main benefit stems from the fact that it allows the evolutionary process to examine more individuals within the same computational budget, even though each individual is examined less completely.