Directed evolution is a versatile technique in protein engineering that mimics the process of natural selection by iteratively alternating between mutagenesis and screening in order to search for sequences that optimize a given property of interest, such as catalytic activity and binding affinity to a specified target. However, the space of possible proteins is too large to search exhaustively in the laboratory, and functional proteins are scarce in the vast sequence space. Machine learning (ML) approaches can accelerate directed evolution by learning to map protein sequences to functions without building a detailed model of the underlying physics, chemistry and biological pathways. Despite the great potentials held by these ML methods, they encounter severe challenges in identifying the most suitable sequences for a targeted function. These failures can be attributed to the common practice of adopting a high-dimensional feature representation for protein sequences and inefficient search methods. To address these issues, we propose an efficient, experimental design-oriented closed-loop optimization framework for protein directed evolution, termed ODBO, which employs a combination of novel low-dimensional protein encoding strategy and Bayesian optimization enhanced with search space prescreening via outlier detection. We further design an initial sample selection strategy to minimize the number of experimental samples for training ML models. We conduct and report four protein directed evolution experiments that substantiate the capability of the proposed framework for finding of the variants with properties of interest. We expect the ODBO framework to greatly reduce the experimental cost and time cost of directed evolution, and can be further generalized as a powerful tool for adaptive experimental design in a broader context.

A novel approach to efficiently treat pure-state equality constraints in optimal control problems (OCPs) using a Riccati recursion algorithm is proposed. The proposed method transforms a pure-state equality constraint into a mixed state-control constraint such that the constraint is expressed by variables at a certain previous time stage. It is showed that if the solution satisfies the second-order sufficient conditions of the OCP with the transformed mixed state-control constraints, it is a local minimum of the OCP with the original pure-state constraints. A Riccati recursion algorithm is derived to solve the OCP using the transformed constraints with linear time complexity in the grid number of the horizon, in contrast to a previous approach that scales cubically with respect to the total dimension of the pure-state equality constraints. Numerical experiments on the whole-body optimal control of quadrupedal gaits that involve pure-state equality constraints owing to contact switches demonstrate the effectiveness of the proposed method over existing approaches.

Machine learning problems with multiple objective functions appear either in learning with multiple criteria where learning has to make a trade-off between multiple performance metrics such as fairness, safety and accuracy; or, in multi-task learning where multiple tasks are optimized jointly, sharing inductive bias between them. This problems are often tackled by the multi-objective optimization framework. However, existing stochastic multi-objective gradient methods and its variants (e.g., MGDA, PCGrad, CAGrad, etc.) all adopt a biased noisy gradient direction, which leads to degraded empirical performance. To this end, we develop a stochastic Multi-objective gradient Correction (MoCo) method for multi-objective optimization. The unique feature of our method is that it can guarantee convergence without increasing the batch size even in the non-convex setting. Simulations on multi-task supervised and reinforcement learning demonstrate the effectiveness of our method relative to state-of-the-art methods.

Polynomial Networks (PNs) have demonstrated promising performance on face and image recognition recently. However, robustness of PNs is unclear and thus obtaining certificates becomes imperative for enabling their adoption in real-world applications. Existing verification algorithms on ReLU neural networks (NNs) based on classical branch and bound (BaB) techniques cannot be trivially applied to PN verification. In this work, we devise a new bounding method, equipped with BaB for global convergence guarantees, called Verification of Polynomial Networks or VPN for short. One key insight is that we obtain much tighter bounds than the interval bound propagation (IBP) and DeepT-Fast [Bonaert et al., 2021] baselines. This enables sound and complete PN verification with empirical validation on MNIST, CIFAR10 and STL10 datasets. We believe our method has its own interest to NN verification.

Recent studies have shown that gradient descent (GD) can achieve improved generalization when its dynamics exhibits a chaotic behavior. However, to obtain the desired effect, the step-size should be chosen sufficiently large, a task which is problem dependent and can be difficult in practice. In this study, we incorporate a chaotic component to GD in a controlled manner, and introduce multiscale perturbed GD (MPGD), a novel optimization framework where the GD recursion is augmented with chaotic perturbations that evolve via an independent dynamical system. We analyze MPGD from three different angles: (i) By building up on recent advances in rough paths theory, we show that, under appropriate assumptions, as the step-size decreases, the MPGD recursion converges weakly to a stochastic differential equation (SDE) driven by a heavy-tailed L\'evy-stable process. (ii) By making connections to recently developed generalization bounds for heavy-tailed processes, we derive a generalization bound for the limiting SDE and relate the worst-case generalization error over the trajectories of the process to the parameters of MPGD. (iii) We analyze the implicit regularization effect brought by the dynamical regularization and show that, in the weak perturbation regime, MPGD introduces terms that penalize the Hessian of the loss function. Empirical results are provided to demonstrate the advantages of MPGD.

We propose cooperative edge-assisted dynamic federated learning (CE-FL). CE-FL introduces a distributed machine learning (ML) architecture, where data collection is carried out at the end devices, while the model training is conducted cooperatively at the end devices and the edge servers, enabled via data offloading from the end devices to the edge servers through base stations. CE-FL also introduces floating aggregation point, where the local models generated at the devices and the servers are aggregated at an edge server, which varies from one model training round to another to cope with the network evolution in terms of data distribution and users' mobility. CE-FL considers the heterogeneity of network elements in terms of communication/computation models and the proximity to one another. CE-FL further presumes a dynamic environment with online variation of data at the network devices which causes a drift at the ML model performance. We model the processes taken during CE-FL, and conduct analytical convergence analysis of its ML model training. We then formulate network-aware CE-FL which aims to adaptively optimize all the network elements via tuning their contribution to the learning process, which turns out to be a non-convex mixed integer problem. Motivated by the large scale of the system, we propose a distributed optimization solver to break down the computation of the solution across the network elements. We finally demonstrate the effectiveness of our framework with the data collected from a real-world testbed.

Filter pruning is a common method to achieve model compression and acceleration in deep neural networks (DNNs).Some research regarded filter pruning as a combinatorial optimization problem and thus used evolutionary algorithms (EA) to prune filters of DNNs. However, it is difficult to find a satisfactory compromise solution in a reasonable time due to the complexity of solution space searching. To solve this problem, we first formulate a multi-objective optimization problem based on a sub-network of the full model and propose a Sub-network Multiobjective Evolutionary Algorithm (SMOEA) for filter pruning. By progressively pruning the convolutional layers in groups, SMOEA can obtain a lightweight pruned result with better performance.Experiments on VGG-14 model for CIFAR-10 verify the effectiveness of the proposed SMOEA. Specifically, the accuracy of the pruned model with 16.56% parameters decreases by 0.28% only, which is better than the widely used popular filter pruning criteria.

Using machine learning to solve combinatorial optimization (CO) problems is challenging, especially when the data is unlabeled. This work proposes an unsupervised learning framework for CO problems. Our framework follows a standard relaxation-plus-rounding approach and adopts neural networks to parameterize the relaxed solutions so that simple back-propagation can train the model end-to-end. Our key contribution is the observation that if the relaxed objective satisfies entry-wise concavity, a low optimization loss guarantees the quality of the final integral solutions. This observation significantly broadens the applicability of the previous framework inspired by Erdos' probabilistic method. In particular, this observation can guide the design of objective models in applications where the objectives are not given explicitly while requiring being modeled in prior. We evaluate our framework by solving a synthetic graph optimization problem, and two real-world applications including resource allocation in circuit design and approximate computing. Our framework largely outperforms the baselines based on na\"{i}ve relaxation, reinforcement learning, and Gumbel-softmax tricks.

Modern machine learning architectures are often highly expressive. They are usually over-parameterized and can interpolate the data by driving the empirical loss close to zero. We analyze the convergence of Local SGD (or FedAvg) for such over-parameterized models in the heterogeneous data setting and improve upon the existing literature by establishing the following convergence rates. We show an error bound of $\O(\exp(-T))$ for strongly-convex loss functions, where $T$ is the total number of iterations. For general convex loss functions, we establish an error bound of $\O(1/T)$ under a mild data similarity assumption and an error bound of $\O(K/T)$ otherwise, where $K$ is the number of local steps. We also extend our results for non-convex loss functions by proving an error bound of $\O(K/T)$. Before our work, the best-known convergence rate for strongly-convex loss functions was $\O(\exp(-T/K))$, and none existed for general convex or non-convex loss functions under the overparameterized setting. We complete our results by providing problem instances in which such convergence rates are tight to a constant factor under a reasonably small stepsize scheme. Finally, we validate our theoretical results using numerical experiments on real and synthetic data.

Bayesian optimisation (BO) algorithms have shown remarkable success in applications involving expensive black-box functions. Traditionally BO has been set as a sequential decision-making process which estimates the utility of query points via an acquisition function and a prior over functions, such as a Gaussian process. Recently, however, a reformulation of BO via density-ratio estimation (BORE) allowed reinterpreting the acquisition function as a probabilistic binary classifier, removing the need for an explicit prior over functions and increasing scalability. In this paper, we present a theoretical analysis of BORE's regret and an extension of the algorithm with improved uncertainty estimates. We also show that BORE can be naturally extended to a batch optimisation setting by recasting the problem as approximate Bayesian inference. The resulting algorithms come equipped with theoretical performance guarantees and are assessed against other batch and sequential BO baselines in a series of experiments.