We consider a scenario where multiple agents are learning a common decision vector from data which can be influenced by the agents' decisions. This leads to the problem of multi-agent performative prediction (Multi-PfD). In this paper, we formulate Multi-PfD as a decentralized optimization problem that minimizes a sum of loss functions, where each loss function is based on a distribution influenced by the local decision vector. We first prove the necessary and sufficient condition for the Multi-PfD problem to admit a unique multi-agent performative stable (Multi-PS) solution. We show that enforcing consensus leads to a laxer condition for existence of Multi-PS solution with respect to the distributions' sensitivities, compared to the single agent case. Then, we study a decentralized extension to the greedy deployment scheme [Mendler-Dünner et al., 2020], called the DSGD-GD scheme. We show that DSGD-GD converges to the Multi-PS solution and analyze its non asymptotic convergence rate.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. In this problem a subset S_t of available actions of a decision set S\subseteq {0,1}^d is chosen stochastically. Then the algorithm chooses an action v\in S_t and incurs a loss of v^T*l_t where l_t is a loss vector chosen by an oblivious adversary. The paper studies the problem in three settings full information, semi-bandit and a new setting which they term restricted. Results: Previously results were known in the full information and semi-bandit setting with sublinear regret bounds.

This work proposes and studies the distributed resource allocation problem in asynchronous and stochastic settings. We consider a distributed system with multiple workers and a coordinating server with heterogeneous computation and communication times. We explore an approximate stochastic primal-dual approach with the aim of 1) adhering to the resource budget constraints, 2) allowing for the asynchronicity between the workers and the server, and 3) relying on the locally available stochastic gradients. We analyze our Asynchronous stochastic Primal-Dual (Asyn-PD) algorithm and prove its convergence in the second moment to the saddle point solution of the approximate problem at the rate of $O(1/t)$, where $t$ is the iteration number. Furthermore, we verify our algorithm numerically to validate the analytically derived convergence results, and demonstrate the advantages of utilizing our asynchronous algorithm rather than deploying a synchronous algorithm where the server must wait until it gets update from all workers.

We consider a scenario where multiple agents are learning a common decision vector from data which can be influenced by the agents' decisions. This leads to the problem of multi-agent performative prediction (Multi-PfD). In this paper, we formulate Multi-PfD as a decentralized optimization problem that minimizes a sum of loss functions, where each loss function is based on a distribution influenced by the local decision vector. We first prove the necessary and sufficient condition for the Multi-PfD problem to admit a unique multi-agent performative stable (Multi-PS) solution. We show that enforcing consensus leads to a laxer condition for existence of Multi-PS solution with respect to the distributions' sensitivities, compared to the single agent case.

Spacecraft trajectory design is a global search problem, where previous work has revealed specific solution structures that can be captured with data-driven methods. This paper explores two global search problems in the circular restricted three-body problem: hybrid cost function of minimum fuel/time-of-flight and transfers to energy-dependent invariant manifolds. These problems display a fundamental structure either in the optimal control profile or the use of dynamical structures. We build on our prior generative machine learning framework to apply diffusion models to learn the conditional probability distribution of the search problem and analyze the model's capability to capture these structures.

Black-box optimization refers to the optimization problem whose objective function and/or constraint sets are either unknown, inaccessible, or non-existent. In many applications, especially with the involvement of humans, the only way to access the optimization problem is through performing physical experiments with the available outcomes being the preference of one candidate with respect to one or many others. Accordingly, the algorithm so-called Active Preference Learning has been developed to exploit this specific information in constructing a surrogate function based on standard radial basis functions, and then forming an easy-to-solve acquisition function which repetitively suggests new decision vectors to search for the optimal solution. Based on this idea, our approach aims to extend the algorithm in such a way that can exploit further information effectively, which can be obtained in reality such as: 5-point Likert type scale for the outcomes of the preference query (i.e., the preference can be described in not only "this is better than that" but also "this is much better than that" level), or multiple outcomes for a single preference query with possible additive information on how certain the outcomes are. The validation of the proposed algorithm is done through some standard benchmark functions, showing a promising improvement with respect to the state-of-the-art algorithm.

Bayesian optimisation (BO) has been widely used to solve problems with expensive function evaluations. In multi-objective optimisation problems, BO aims to find a set of approximated Pareto optimal solutions. There are typically two ways to build surrogates in multi-objective BO: One surrogate by aggregating objective functions (by using a scalarising function, also called mono-surrogate approach) and multiple surrogates (for each objective function, also called multi-surrogate approach). In both approaches, an acquisition function (AF) is used to guide the search process. Mono-surrogate has the advantage that only one model is used, however, the approach has two major limitations. Firstly, the fitness landscape of the scalarising function and the objective functions may not be similar. Secondly, the approach assumes that the scalarising function distribution is Gaussian, and thus a closed-form expression of the AF can be used. In this work, we overcome these limitations by building a surrogate model for each objective function and show that the scalarising function distribution is not Gaussian. We approximate the distribution using Generalised extreme value distribution. The results and comparison with existing approaches on standard benchmark and real-world optimisation problems show the potential of the multi-surrogate approach.

Many real-world multi-objective optimisation problems rely on computationally expensive function evaluations. Multi-objective Bayesian optimisation (BO) can be used to alleviate the computation time to find an approximated set of Pareto optimal solutions. In many real-world problems, a decision-maker has some preferences on the objective functions. One approach to incorporate the preferences in multi-objective BO is to use a scalarising function and build a single surrogate model (mono-surrogate approach) on it. This approach has two major limitations. Firstly, the fitness landscape of the scalarising function and the objective functions may not be similar. Secondly, the approach assumes that the scalarising function distribution is Gaussian, and thus a closed-form expression of an acquisition function e.g., expected improvement can be used. We overcome these limitations by building independent surrogate models (multi-surrogate approach) on each objective function and show that the distribution of the scalarising function is not Gaussian. We approximate the distribution using Generalised value distribution. We present an a-priori multi-surrogate approach to incorporate the desirable objective function values (or reference point) as the preferences of a decision-maker in multi-objective BO. The results and comparison with the existing mono-surrogate approach on benchmark and real-world optimisation problems show the potential of the proposed approach.

This paper proposes a method for solving optimization problems in which the decision-maker cannot evaluate the objective function, but rather can only express a preference such as "this is better than that" between two candidate decision vectors. The algorithm described in this paper aims at reaching the global optimizer by iteratively proposing the decision maker a new comparison to make, based on actively learning a surrogate of the latent (unknown and perhaps unquantifiable) objective function from past sampled decision vectors and pairwise preferences. The surrogate is fit by means of radial basis functions, under the constraint of satisfying, if possible, the preferences expressed by the decision maker on existing samples. The surrogate is used to propose a new sample of the decision vector for comparison with the current best candidate based on two possible criteria: minimize a combination of the surrogate and an inverse weighting distance function to balance between exploitation of the surrogate and exploration of the decision space, or maximize a function related to the probability that the new candidate will be preferred. Compared to active preference learning based on Bayesian optimization, we show that our approach is superior in that, within the same number of comparisons, it approaches the global optimum more closely and is computationally lighter. MATLAB and a Python implementations of the algorithms described in the paper are available at http://cse.lab.imtlucca.it/~bemporad/idwgopt.

The expected reward in a linear stochastic bandit model is an unknown linear function of the chosen decision vector. In this paper, we consider the case where the expected reward is an unknown linear function of a projection of the decision vector onto a subspace. We call this the projection reward. Unlike the classical linear bandit problem, we assume that the projection reward is unobservable. Instead, the observed "reward" at each time step is the projection reward corrupted by another linear function of the decision vector projected onto a subspace orthogonal to the first. Such a model is useful in recommendation applications where the observed reward is corrupted by each individual's biases. In the case where there are finitely many decision vectors, we develop a strategy to achieve $O(\log T)$ regret, where $T$ is the number of time steps. In the case where the decision vector is chosen from an infinite compact set, our strategy achieves $O(T^{2/3}(\log{T})^{1/2})$ regret. Simulations verify the efficiency of our strategy.