Bayesian optimization has been successfully applied to optimize black-box functions where the number of evaluations is severely limited. However, in many real-world applications, it is hard or impossible to know in advance which designs are feasible due to some physical or system limitations. These issues lead to an even more challenging problem of optimizing an unknown function with unknown constraints. In this paper, we observe that in such scenarios optimal solution typically lies on the boundary between feasible and infeasible regions of the design space, making it considerably more difficult than that with interior optima. Inspired by this observation, we propose BE-CBO, a new Bayesian optimization method that efficiently explores the boundary between feasible and infeasible designs. To identify the boundary, we learn the constraints with an ensemble of neural networks that outperform the standard Gaussian Processes for capturing complex boundaries. Our method demonstrates superior performance against state-of-the-art methods through comprehensive experiments on synthetic and real-world benchmarks.

In recent years, machine learning algorithms have been used in high-stakes decision-making settings, such as healthcare, loan approval, or parole decisions (Baesens et al., 2003; Zeng et al., 2022, 2017). Consequently, there is a growing interest and necessity in their explainability and interpretability (Du et al., 2019; Jung et al., 2020; Molnar et al., 2020; Rudin et al., 2022; Zhang et al., 2019). Once a supervised classification model has been trained, one may be interested in knowing the changes needed to be made in the features of an instance to change the prediction made by the classifier. These changes are the so-called counterfactual explanations (Martens and Provost, 2014; Wachter et al., 2017). There is a growing literature on the development of algorithms to generate counterfactual explanations, see Artelt and Hammer (2019); Guidotti (2022); Karimi et al. (2022); Sokol and Flach (2019); Stepin et al. (2021); Verma et al. (2022) for recent surveys on Counterfactual Analysis. Nevertheless, they mainly focus on the single-instance, single-counterfactual case, where for one specific instance, a single counterfactual is provided (Wachter et al., 2017; Parmentier and Vidal, 2021).

We propose and analyze an adaptive adversary that can retrain a Trojaned DNN and is also aware of SOTA output-based Trojaned model detectors. We show that such an adversary can ensure (1) high accuracy on both trigger-embedded and clean samples and (2) bypass detection. Our approach is based on an observation that the high dimensionality of the DNN parameters provides sufficient degrees of freedom to simultaneously achieve these objectives. We also enable SOTA detectors to be adaptive by allowing retraining to recalibrate their parameters, thus modeling a co-evolution of parameters of a Trojaned model and detectors. We then show that this co-evolution can be modeled as an iterative game, and prove that the resulting (optimal) solution of this interactive game leads to the adversary successfully achieving the above objectives. In addition, we provide a greedy algorithm for the adversary to select a minimum number of input samples for embedding triggers. We show that for cross-entropy or log-likelihood loss functions used by the DNNs, the greedy algorithm provides provable guarantees on the needed number of trigger-embedded input samples. Extensive experiments on four diverse datasets -- MNIST, CIFAR-10, CIFAR-100, and SpeechCommand -- reveal that the adversary effectively evades four SOTA output-based Trojaned model detectors: MNTD, NeuralCleanse, STRIP, and TABOR.

We study two variants of the mirror descent-ascent algorithm for solving min-max problems on the space of measures: simultaneous and sequential. We work under assumptions of convexity-concavity and relative smoothness of the payoff function with respect to a suitable Bregman divergence, defined on the space of measures via flat derivatives. We show that the convergence rates to mixed Nash equilibria, measured in the Nikaid\`o-Isoda error, are of order $\mathcal{O}\left(N^{-1/2}\right)$ and $\mathcal{O}\left(N^{-2/3}\right)$ for the simultaneous and sequential schemes, respectively, which is in line with the state-of-the-art results for related finite-dimensional algorithms.

In this paper, we focus on simple bilevel optimization problems, where we minimize a convex smooth objective function over the optimal solution set of another convex smooth constrained optimization problem. We present a novel bilevel optimization method that locally approximates the solution set of the lower-level problem using a cutting plane approach and employs an accelerated gradient-based update to reduce the upper-level objective function over the approximated solution set. We measure the performance of our method in terms of suboptimality and infeasibility errors and provide non-asymptotic convergence guarantees for both error criteria. Specifically, when the feasible set is compact, we show that our method requires at most $\mathcal{O}(\max\{1/\sqrt{\epsilon_{f}}, 1/\epsilon_g\})$ iterations to find a solution that is $\epsilon_f$-suboptimal and $\epsilon_g$-infeasible. Moreover, under the additional assumption that the lower-level objective satisfies the $r$-th H\"olderian error bound, we show that our method achieves an iteration complexity of $\mathcal{O}(\max\{\epsilon_{f}^{-\frac{2r-1}{2r}},\epsilon_{g}^{-\frac{2r-1}{2r}}\})$, which matches the optimal complexity of single-level convex constrained optimization when $r=1$.

Morpho-evolution (ME) refers to the simultaneous optimisation of a robot's design and controller to maximise performance given a task and environment. Many genetic encodings have been proposed which are capable of representing design and control. Previous research has provided empirical comparisons between encodings in terms of their performance with respect to an objective function and the diversity of designs that are evaluated, however there has been no attempt to explain the observed findings. We address this by applying Local Optima Network (LON) analysis to investigate the structure of the fitness landscapes induced by three different encodings when evolving a robot for a locomotion task, shedding new light on the ease by which different fitness landscapes can be traversed by a search process. This is the first time LON analysis has been applied in the field of ME despite its popularity in combinatorial optimisation domains; the findings will facilitate design of new algorithms or operators that are customised to ME landscapes in the future.

Large-scale machine learning problems make the cost of hyperparameter tuning ever more prohibitive. This creates a need for algorithms that can tune themselves on-the-fly. We formalize the notion of "tuning-free" algorithms that can match the performance of optimally-tuned optimization algorithms up to polylogarithmic factors given only loose hints on the relevant problem parameters. We consider in particular algorithms that can match optimally-tuned Stochastic Gradient Descent (SGD). When the domain of optimization is bounded, we show tuning-free matching of SGD is possible and achieved by several existing algorithms. We prove that for the task of minimizing a convex and smooth or Lipschitz function over an unbounded domain, tuning-free optimization is impossible. We discuss conditions under which tuning-free optimization is possible even over unbounded domains. In particular, we show that the recently proposed DoG and DoWG algorithms are tuning-free when the noise distribution is sufficiently well-behaved. For the task of finding a stationary point of a smooth and potentially nonconvex function, we give a variant of SGD that matches the best-known high-probability convergence rate for tuned SGD at only an additional polylogarithmic cost. However, we also give an impossibility result that shows no algorithm can hope to match the optimal expected convergence rate for tuned SGD with high probability.

Many decision processes in artificial intelligence and operations research are modeled by parametric optimization problems whose defining parameters are unknown and must be inferred from observable data. The Predict-Then-Optimize (PtO) paradigm in machine learning aims to maximize downstream decision quality by training the parametric inference model end-to-end with the subsequent constrained optimization. This requires backpropagation through the optimization problem using approximation techniques specific to the problem's form, especially for nondifferentiable linear and mixed-integer programs. This paper extends the PtO methodology to optimization problems with nondifferentiable Ordered Weighted Averaging (OWA) objectives, known for their ability to ensure properties of fairness and robustness in decision models. Through a collection of training techniques and proposed application settings, it shows how optimization of OWA functions can be effectively integrated with parametric prediction for fair and robust optimization under uncertainty.

In the field of online sequential decision-making, we address the problem with delays utilizing the framework of online convex optimization (OCO), where the feedback of a decision can arrive with an unknown delay. Unlike previous research that is limited to Euclidean norm and gradient information, we propose three families of delayed algorithms based on approximate solutions to handle different types of received feedback. Our proposed algorithms are versatile and applicable to universal norms. Specifically, we introduce a family of Follow the Delayed Regularized Leader algorithms for feedback with full information on the loss function, a family of Delayed Mirror Descent algorithms for feedback with gradient information on the loss function and a family of Simplified Delayed Mirror Descent algorithms for feedback with the value information of the loss function's gradients at corresponding decision points. For each type of algorithm, we provide corresponding regret bounds under cases of general convexity and relative strong convexity, respectively. We also demonstrate the efficiency of each algorithm under different norms through concrete examples. Furthermore, our theoretical results are consistent with the current best bounds when degenerated to standard settings.

Recent representation learning approaches enhance neural topic models by optimizing the weighted linear combination of the evidence lower bound (ELBO) of the log-likelihood and the contrastive learning objective that contrasts pairs of input documents. However, document-level contrastive learning might capture low-level mutual information, such as word ratio, which disturbs topic modeling. Moreover, there is a potential conflict between the ELBO loss that memorizes input details for better reconstruction quality, and the contrastive loss which attempts to learn topic representations that generalize among input documents. To address these issues, we first introduce a novel contrastive learning method oriented towards sets of topic vectors to capture useful semantics that are shared among a set of input documents. Secondly, we explicitly cast contrastive topic modeling as a gradient-based multi-objective optimization problem, with the goal of achieving a Pareto stationary solution that balances the trade-off between the ELBO and the contrastive objective. Extensive experiments demonstrate that our framework consistently produces higher-performing neural topic models in terms of topic coherence, topic diversity, and downstream performance. In recent years, Variational Autoencoder (VAE) (Kingma & Welling, 2013) has achieved great success in many fields, and its encoder-decoder architecture has been inherited for topic modeling with neural networks, dubbed as Neural Topic Model (NTM) (Miao et al., 2016).