hypervolume
BOAT: Navigating the Sea of In Silico Predictors for Antibody Design via Multi-Objective Bayesian Optimization
Rao, Jackie, Hernandez, Ferran Gonzalez, Gerard, Leon, Gessner, Alexandra
Antibody lead optimization is inherently a multi-objective challenge in drug discovery. Achieving a balance between different drug-like properties is crucial for the development of viable candidates, and this search becomes exponentially challenging as desired properties grow. The ever-growing zoo of sophisticated in silico tools for predicting antibody properties calls for an efficient joint optimization procedure to overcome resource-intensive sequential filtering pipelines. We present BOAT, a versatile Bayesian optimization framework for multi-property antibody engineering. Our `plug-and-play' framework couples uncertainty-aware surrogate modeling with a genetic algorithm to jointly optimize various predicted antibody traits while enabling efficient exploration of sequence space. Through systematic benchmarking against genetic algorithms and newer generative learning approaches, we demonstrate competitive performance with state-of-the-art methods for multi-objective protein optimization. We identify clear regimes where surrogate-driven optimization outperforms expensive generative approaches and establish practical limits imposed by sequence dimensionality and oracle costs.
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Hypervolume Maximization: A Geometric View of Pareto Set Learning
This paper presents a novel approach to multiobjective algorithms aimed at modeling the Pareto set using neural networks. Whereas previous methods mainly focused on identifying a finite number of solutions, our approach allows for the direct modeling of the entire Pareto set. Furthermore, we establish an equivalence between learning the complete Pareto set and maximizing the associated hypervolume, which enables the convergence analysis of hypervolume (as a new metric) for Pareto set learning. Specifically, our new analysis framework reveals the connection between the learned Pareto solution and its representation in a polar coordinate system. We evaluate our proposed approach on various benchmark problems and real-world problems, and the encouraging results make it a potentially viable alternative to existing multiobjective algorithms.
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Evolved SampleWeights for Bias Mitigation: Effectiveness Depends on Optimization Objectives
Saini, Anil K., Hernandez, Jose Guadalupe, Wong, Emily F., Misra, Debanshi, Moore, Jason H.
Machine learning models trained on real-world data may inadvertently make biased predictions that negatively impact marginalized communities. Reweighting is a method that can mitigate such bias in model predictions by assigning a weight to each data point used during model training. In this paper, we compare three methods for generating these weights: (1) evolving them using a Genetic Algorithm (GA), (2) computing them using only dataset characteristics, and (3) assigning equal weights to all data points. Model performance under each strategy was evaluated using paired predictive and fairness metrics, which also served as optimization objectives for the GA during evolution. Specifically, we used two predictive metrics (accuracy and area under the Receiver Operating Characteristic curve) and two fairness metrics (demographic parity difference and subgroup false negative fairness). Using experiments on eleven publicly available datasets (including two medical datasets), we show that evolved sample weights can produce models that achieve better trade-offs between fairness and predictive performance than alternative weighting methods. However, the magnitude of these benefits depends strongly on the choice of optimization objectives. Our experiments reveal that optimizing with accuracy and demographic parity difference metrics yields the largest number of datasets for which evolved weights are significantly better than other weighting strategies in optimizing both objectives.
Limitations of Scalarisation in MORL: A Comparative Study in Discrete Environments
Shah, Muhammad Sa'ood, Jeewa, Asad
Scalarisation functions are widely employed in MORL algorithms to enable intelligent decision-making. However, these functions often struggle to approximate the Pareto front accurately, rendering them unideal in complex, uncertain environments. This study examines selected Multi-Objective Reinforcement Learning (MORL) algorithms across MORL environments with discrete action and observation spaces. We aim to investigate further the limitations associated with scalarisation approaches for decision-making in multi-objective settings. Specifically, we use an outer-loop multi-policy methodology to assess the performance of a seminal single-policy MORL algorithm, MO Q-Learning implemented with linear scalarisation and Chebyshev scalarisation functions. In addition, we explore a pioneering inner-loop multi-policy algorithm, Pareto Q-Learning, which offers a more robust alternative. Our findings reveal that the performance of the scalarisation functions is highly dependent on the environment and the shape of the Pareto front. These functions often fail to retain the solutions uncovered during learning and favour finding solutions in certain regions of the solution space. Moreover, finding the appropriate weight configurations to sample the entire Pareto front is complex, limiting their applicability in uncertain settings. In contrast, inner-loop multi-policy algorithms may provide a more sustainable and generalizable approach and potentially facilitate intelligent decision-making in dynamic and uncertain environments.
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SPREAD: Sampling-based Pareto front Refinement via Efficient Adaptive Diffusion
Hotegni, Sedjro Salomon, Peitz, Sebastian
Developing efficient multi-objective optimization methods to compute the Pareto set of optimal compromises between conflicting objectives remains a key challenge, especially for large-scale and expensive problems. To bridge this gap, we introduce SPREAD, a generative framework based on Denoising Diffusion Probabilistic Models (DDPMs). SPREAD first learns a conditional diffusion process over points sampled from the decision space and then, at each reverse diffusion step, refines candidates via a sampling scheme that uses an adaptive multiple gradient descent-inspired update for fast convergence alongside a Gaussian RBF-based repulsion term for diversity. Empirical results on multi-objective optimization benchmarks, including offline and Bayesian surrogate-based settings, show that SPREAD matches or exceeds leading baselines in efficiency, scalability, and Pareto front coverage.
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Market Making Strategies with Reinforcement Learning
This thesis presents the results of a comprehensive research project focused on applying Reinforcement Learning (RL) to the problem of market making in financial markets. Market makers (MMs) play a fundamental role in providing liquidity, yet face significant challenges arising from inventory risk, competition, and non-stationary market dynamics. This research explores how RL, particularly Deep Reinforcement Learning (DRL), can be employed to develop autonomous, adaptive, and profitable market making strategies. The study begins by formulating the MM task as a reinforcement learning problem, designing agents capable of operating in both single-agent and multi-agent settings within a simulated financial environment. It then addresses the complex issue of inventory management using two complementary approaches: reward engineering and Multi-Objective Reinforcement Learning (MORL). While the former uses dynamic reward shaping to guide behavior, the latter leverages Pareto front optimization to explicitly balance competing objectives. To address the problem of non-stationarity, the research introduces POW-dTS, a novel policy weighting algorithm based on Discounted Thompson Sampling. This method allows agents to dynamically select and combine pretrained policies, enabling continual adaptation to shifting market conditions. The experimental results demonstrate that the proposed RL-based approaches significantly outperform traditional and baseline algorithmic strategies across various performance metrics. Overall, this research thesis contributes new methodologies and insights for the design of robust, efficient, and adaptive market making agents, reinforcing the potential of RL to transform algorithmic trading in complex financial systems.
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