# Evolutionary Systems

### Researchers propose paradigm that trains AI agents through evolution

A paper published by researchers at Carnegie Mellon University, San Francisco research firm OpenAI, Facebook AI Research, the University of California at Berkeley, and Shanghai Jiao Tong University describes a paradigm that scales up multi-agent reinforcement learning, where AI models learn by having agents interact within an environment such that the agent population increases in size over time. By maintaining sets of agents in each training stage and performing mix-and-match and fine-tuning steps over these sets, the coauthors say the paradigm -- Evolutionary Population Curriculum -- is able to promote agents with the best adaptability to the next stage. In computer science, evolutionary computation is the family of algorithms for global optimization inspired by biological evolution. Instead of following explicit mathematical gradients, these models generate variants, test them, and retain the top performers. They've shown promise in early work by OpenAI, Google, Uber, and others, but they're somewhat tough to prototype because there's a dearth of tools targeting evolutionary algorithms and natural evolution strategies (NES).

### Average Individual Fairness: Algorithms, Generalization and Experiments

We propose a new family of fairness definitions for classification problems that combine some of the best properties of both statistical and individual notions of fairness. We then ask that standard statistics (such as error or false positive/negative rates) be (approximately) equalized across individuals, where the rate is defined as an expectation over the classification tasks. Because we are no longer averaging over coarse groups (such as race or gender), this is a semantically meaningful individual-level constraint. Given a sample of individuals and problems, we design an oracle-efficient algorithm (i.e. one that is given access to any standard, fairness-free learning heuristic) for the fair empirical risk minimization task. We also show that given sufficiently many samples, the ERM solution generalizes in two directions: both to new individuals, and to new classification tasks, drawn from their corresponding distributions.

### Generalization Error Analysis of Quantized Compressive Learning

Compressive learning is an effective method to deal with very high dimensional datasets by applying learning algorithms in a randomly projected lower dimensional space. In this paper, we consider the learning problem where the projected data is further compressed by scalar quantization, which is called quantized compressive learning. Generalization error bounds are derived for three models: nearest neighbor (NN) classifier, linear classifier and least squares regression. Besides studying finite sample setting, our asymptotic analysis shows that the inner product estimators have deep connection with NN and linear classification problem through the variance of their debiased counterparts. By analyzing the extra error term brought by quantization, our results provide useful implications to the choice of quantizers in applications involving different learning tasks.

### Algorithm-Dependent Generalization Bounds for Overparameterized Deep Residual Networks

The skip-connections used in residual networks have become a standard architecture choice in deep learning due to the increased generalization and stability of networks with this architecture, although there have been limited theoretical guarantees for this improved performance. In this work, we analyze overparameterized deep residual networks trained by gradient descent following random initialization, and demonstrate that (i) the class of networks learned by gradient descent constitutes a small subset of the entire neural network function class, and (ii) this subclass of networks is sufficiently large to guarantee small training error. By showing (i) we are able to demonstrate that deep residual networks trained with gradient descent have a small generalization gap between training and test error, and together with (ii) this guarantees that the test error will be small. Our optimization and generalization guarantees require overparameterization that is only logarithmic in the depth of the network, which helps explain why residual networks are preferable to fully connected ones. Papers published at the Neural Information Processing Systems Conference.

### Generalization Bounds in the Predict-then-Optimize Framework

The predict-then-optimize framework is fundamental in many practical settings: predict the unknown parameters of an optimization problem, and then solve the problem using the predicted values of the parameters. A natural loss function in this environment is to consider the cost of the decisions induced by the predicted parameters, in contrast to the prediction error of the parameters. This loss function was recently introduced in [Elmachtoub and Grigas, 2017], which called it the Smart Predict-then-Optimize (SPO) loss. Since the SPO loss is nonconvex and noncontinuous, standard results for deriving generalization bounds do not apply. In this work, we provide an assortment of generalization bounds for the SPO loss function.

### Generalization Bounds for Neural Networks via Approximate Description Length

We investigate the sample complexity of networks with bounds on the magnitude of its weights. This bound is optimal up to log-factors, and substantially improves over the previous state of the art of $\tilde O\left(\frac{d 2R 2}{\epsilon 2}\right)$, that was established in a recent line of work. To establish our results we develop a new technique to analyze the sample complexity of families $\ch$ of predictors. We start by defining a new notion of a randomized approximate description of functions $f:\cx\to\reals d$. We then show that if there is a way to approximately describe functions in a class $\ch$ using $d$ bits, then $\frac{d}{\epsilon 2}$ examples suffices to guarantee uniform convergence.

### Generalization of Reinforcement Learners with Working and Episodic Memory

Memory is an important aspect of intelligence and plays a role in many deep reinforcement learning models. However, little progress has been made in understanding when specific memory systems help more than others and how well they generalize. The field also has yet to see a prevalent consistent and rigorous approach for evaluating agent performance on holdout data. In this paper, we aim to develop a comprehensive methodology to test different kinds of memory in an agent and assess how well the agent can apply what it learns in training to a holdout set that differs from the training set along dimensions that we suggest are relevant for evaluating memory-specific generalization. To that end, we first construct a diverse set of memory tasks that allow us to evaluate test-time generalization across multiple dimensions.

### Margin-Based Generalization Lower Bounds for Boosted Classifiers

Boosting is one of the most successful ideas in machine learning. The most well-accepted explanations for the low generalization error of boosting algorithms such as AdaBoost stem from margin theory. The study of margins in the context of boosting algorithms was initiated by Schapire, Freund, Bartlett and Lee (1998), and has inspired numerous boosting algorithms and generalization bounds. To date, the strongest known generalization (upper bound) is the $k$th margin bound of Gao and Zhou (2013). Despite the numerous generalization upper bounds that have been proved over the last two decades, nothing is known about the tightness of these bounds.

### Uniform convergence may be unable to explain generalization in deep learning

Aimed at explaining the surprisingly good generalization behavior of overparameterized deep networks, recent works have developed a variety of generalization bounds for deep learning, all based on the fundamental learning-theoretic technique of uniform convergence. While it is well-known that many of these existing bounds are numerically large, through numerous experiments, we bring to light a more concerning aspect of these bounds: in practice, these bounds can {\em increase} with the training dataset size. Guided by our observations, we then present examples of overparameterized linear classifiers and neural networks trained by gradient descent (GD) where uniform convergence provably cannot explain generalization'' -- even if we take into account the implicit bias of GD {\em to the fullest extent possible}. More precisely, even if we consider only the set of classifiers output by GD, which have test errors less than some small $\epsilon$ in our settings, we show that applying (two-sided) uniform convergence on this set of classifiers will yield only a vacuous generalization guarantee larger than $1-\epsilon$. Through these findings, we cast doubt on the power of uniform convergence-based generalization bounds to provide a complete picture of why overparameterized deep networks generalize well.

### A Necessary and Sufficient Stability Notion for Adaptive Generalization

We introduce a new notion of the stability of computations, which holds under post-processing and adaptive composition. We show that the notion is both necessary and sufficient to ensure generalization in the face of adaptivity, for any computations that respond to bounded-sensitivity linear queries while providing accuracy with respect to the data sample set. The stability notion is based on quantifying the effect of observing a computation's outputs on the posterior over the data sample elements. We show a separation between this stability notion and previously studied notion and observe that all differentially private algorithms also satisfy this notion. Papers published at the Neural Information Processing Systems Conference.