Bayesian optimization (BO) is a popular tool for optimizing complex and costly-to-evaluate blackb... more Bayesian optimization (BO) is a popular tool for optimizing complex and costly-to-evaluate blackbox objective functions. To further reduce the number of function evaluations, any party performing BO may be interested to collaborate with others to optimize the same objective function concurrently. To do this, existing BO algorithms have considered optimizing a batch of input queries in parallel and provided theoretical bounds on their cumulative regret reflecting inefficiency. However, when the objective function values are correlated with real-world rewards (e.g., money), parties may be hesitant to collaborate if they risk incurring larger cumulative regret (i.e., smaller real-world reward) than others. This paper shows that fairness and efficiency are both necessary for the collaborative BO setting. Inspired by social welfare concepts from economics, we propose a new notion of regret capturing these properties and a collaborative BO algorithm whose convergence rate can be theoretic...
Collaborative machine learning (ML) is an appealing paradigm to build high-quality ML models by t... more Collaborative machine learning (ML) is an appealing paradigm to build high-quality ML models by training on the aggregated data from many parties. However, these parties are only willing to share their data when given enough incentives, such as a guaranteed fair reward based on their contributions. This motivates the need for measuring a party's contribution and designing an incentive-aware reward scheme accordingly. This paper proposes to value a party's reward based on Shapley value and information gain on model parameters given its data. Subsequently, we give each party a model as a reward. To formally incentivize the collaboration, we define some desirable properties (e.g., fairness and stability) which are inspired by cooperative game theory but adapted for our model reward that is uniquely freely replicable. Then, we propose a novel model reward scheme to satisfy fairness and trade off between the desirable properties via an adjustable parameter. The value of each part...
Proceedings of the AAAI Conference on Artificial Intelligence, 2020
This paper presents a variational Bayesian kernel selection (VBKS) algorithm for sparse Gaussian ... more This paper presents a variational Bayesian kernel selection (VBKS) algorithm for sparse Gaussian process regression (SGPR) models. In contrast to existing GP kernel selection algorithms that aim to select only one kernel with the highest model evidence, our VBKS algorithm considers the kernel as a random variable and learns its belief from data such that the uncertainty of the kernel can be interpreted and exploited to avoid overconfident GP predictions. To achieve this, we represent the probabilistic kernel as an additional variational variable in a variational inference (VI) framework for SGPR models where its posterior belief is learned together with that of the other variational variables (i.e., inducing variables and kernel hyperparameters). In particular, we transform the discrete kernel belief into a continuous parametric distribution via reparameterization in order to apply VI. Though it is computationally challenging to jointly optimize a large number of hyperparameters due...
This paper presents a novel generalization of predictive entropy search (PES) for multi-fidelity ... more This paper presents a novel generalization of predictive entropy search (PES) for multi-fidelity Bayesian optimization (BO) called multi-fidelity PES (MF-PES). In contrast to existing multi-fidelity BO algorithms, our proposed MF-PES algorithm can naturally trade off between exploitation vs. exploration over the target and auxiliary functions with varying fidelities without needing to manually tune any such parameters or input discretization. To achieve this, we first model the unknown target and auxiliary functions jointly as a convolved multi-output Gaussian process (CMOGP) whose convolutional structure is then exploited for deriving an efficient approximation of MF-PES. Empirical evaluation on synthetic and real-world experiments shows that MF-PES outperforms the state-of-the-art multi-fidelity BO algorithms.
This paper presents novel mixed-type Bayesian optimization (BO) algorithms to accelerate the opti... more This paper presents novel mixed-type Bayesian optimization (BO) algorithms to accelerate the optimization of a target objective function by exploiting correlated auxiliary information of binary type that can be more cheaply obtained, such as in policy search for reinforcement learning and hyperparameter tuning of machine learning models with early stopping. To achieve this, we first propose a mixed-type multi-output Gaussian process (MOGP) to jointly model the continuous target function and binary auxiliary functions. Then, we propose information-based acquisition functions such as mixed-type entropy search (MT-ES) and mixed-type predictive ES (MT-PES) for mixed-type BO based on the MOGP predictive belief of the target and auxiliary functions. The exact acquisition functions of MT-ES and MT-PES cannot be computed in closed form and need to be approximated. We derive an efficient approximation of MT-PES via a novel mixed-type random features approximation of the MOGP model whose cros...
Bayesian optimization (BO) is a popular tool for optimizing complex and costly-to-evaluate blackb... more Bayesian optimization (BO) is a popular tool for optimizing complex and costly-to-evaluate blackbox objective functions. To further reduce the number of function evaluations, any party performing BO may be interested to collaborate with others to optimize the same objective function concurrently. To do this, existing BO algorithms have considered optimizing a batch of input queries in parallel and provided theoretical bounds on their cumulative regret reflecting inefficiency. However, when the objective function values are correlated with real-world rewards (e.g., money), parties may be hesitant to collaborate if they risk incurring larger cumulative regret (i.e., smaller real-world reward) than others. This paper shows that fairness and efficiency are both necessary for the collaborative BO setting. Inspired by social welfare concepts from economics, we propose a new notion of regret capturing these properties and a collaborative BO algorithm whose convergence rate can be theoretic...
Collaborative machine learning (ML) is an appealing paradigm to build high-quality ML models by t... more Collaborative machine learning (ML) is an appealing paradigm to build high-quality ML models by training on the aggregated data from many parties. However, these parties are only willing to share their data when given enough incentives, such as a guaranteed fair reward based on their contributions. This motivates the need for measuring a party's contribution and designing an incentive-aware reward scheme accordingly. This paper proposes to value a party's reward based on Shapley value and information gain on model parameters given its data. Subsequently, we give each party a model as a reward. To formally incentivize the collaboration, we define some desirable properties (e.g., fairness and stability) which are inspired by cooperative game theory but adapted for our model reward that is uniquely freely replicable. Then, we propose a novel model reward scheme to satisfy fairness and trade off between the desirable properties via an adjustable parameter. The value of each part...
Proceedings of the AAAI Conference on Artificial Intelligence, 2020
This paper presents a variational Bayesian kernel selection (VBKS) algorithm for sparse Gaussian ... more This paper presents a variational Bayesian kernel selection (VBKS) algorithm for sparse Gaussian process regression (SGPR) models. In contrast to existing GP kernel selection algorithms that aim to select only one kernel with the highest model evidence, our VBKS algorithm considers the kernel as a random variable and learns its belief from data such that the uncertainty of the kernel can be interpreted and exploited to avoid overconfident GP predictions. To achieve this, we represent the probabilistic kernel as an additional variational variable in a variational inference (VI) framework for SGPR models where its posterior belief is learned together with that of the other variational variables (i.e., inducing variables and kernel hyperparameters). In particular, we transform the discrete kernel belief into a continuous parametric distribution via reparameterization in order to apply VI. Though it is computationally challenging to jointly optimize a large number of hyperparameters due...
This paper presents a novel generalization of predictive entropy search (PES) for multi-fidelity ... more This paper presents a novel generalization of predictive entropy search (PES) for multi-fidelity Bayesian optimization (BO) called multi-fidelity PES (MF-PES). In contrast to existing multi-fidelity BO algorithms, our proposed MF-PES algorithm can naturally trade off between exploitation vs. exploration over the target and auxiliary functions with varying fidelities without needing to manually tune any such parameters or input discretization. To achieve this, we first model the unknown target and auxiliary functions jointly as a convolved multi-output Gaussian process (CMOGP) whose convolutional structure is then exploited for deriving an efficient approximation of MF-PES. Empirical evaluation on synthetic and real-world experiments shows that MF-PES outperforms the state-of-the-art multi-fidelity BO algorithms.
This paper presents novel mixed-type Bayesian optimization (BO) algorithms to accelerate the opti... more This paper presents novel mixed-type Bayesian optimization (BO) algorithms to accelerate the optimization of a target objective function by exploiting correlated auxiliary information of binary type that can be more cheaply obtained, such as in policy search for reinforcement learning and hyperparameter tuning of machine learning models with early stopping. To achieve this, we first propose a mixed-type multi-output Gaussian process (MOGP) to jointly model the continuous target function and binary auxiliary functions. Then, we propose information-based acquisition functions such as mixed-type entropy search (MT-ES) and mixed-type predictive ES (MT-PES) for mixed-type BO based on the MOGP predictive belief of the target and auxiliary functions. The exact acquisition functions of MT-ES and MT-PES cannot be computed in closed form and need to be approximated. We derive an efficient approximation of MT-PES via a novel mixed-type random features approximation of the MOGP model whose cros...
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Papers by Yehong Zhang