Predictive Entropy Search for Bayesian optimization with unknown constraints

Unknown constraints arise in many types of expensive black-box optimization problems. Several methods have been proposed recently for performing Bayesian optimization with constraints, based on the expected improvement (EI) heuristic. However, EI can lead to pathologies when used with constraints. For example, in the case of decoupled constraints---i.e., when one can independently evaluate the objective or the constraints---EI can encounter a pathology that prevents exploration. Additionally, computing EI requires a current best solution, which may not exist if none of the data collected so far satisfy the constraints. By contrast, information-based approaches do not suffer from these failure modes. In this paper, we present a new information-based method called Predictive Entropy Search with Constraints (PESC). We analyze the performance of PESC and show that it compares favorably to EI-based approaches on synthetic and benchmark problems, as well as several real-world examples. We demonstrate that PESC is an effective algorithm that provides a promising direction towards a unified solution for constrained Bayesian optimization.José Miguel Hernández-Lobato acknowledges support from the Rafael del Pino Foundation. Zoubin Ghahramani acknowledges support from Google Focused Research Award and EPSRC grant EP/I036575/1. Matthew W. Hoffman acknowledges support from EPSRC grant EP/J012300/1.This is the final published version. It first appeared at http://jmlr.org/proceedings/papers/v37/hernandez-lobatob15.html

A General Framework for Constrained Bayesian Optimization using Information-based Search

We present an information-theoretic framework for solving global black-box optimization problems that also have black-box constraints. Of particular interest to us is to efficiently solve problems with $\textit{decoupled}$ constraints, in which subsets of the objective and constraint functions may be evaluated independently. For example, when the objective is evaluated on a CPU and the constraints are evaluated independently on a GPU. These problems require an acquisition function that can be separated into the contributions of the individual function evaluations. We develop one such acquisition function and call it Predictive Entropy Search with Constraints (PESC). PESC is an approximation to the expected information gain criterion and it compares favorably to alternative approaches based on improvement in several synthetic and real-world problems. In addition to this, we consider problems with a mix of functions that are fast and slow to evaluate. These problems require balancing the amount of time spent in the meta-computation of PESC and in the actual evaluation of the target objective. We take a bounded rationality approach and develop a partial update for PESC which trades off accuracy against speed. We then propose a method for adaptively switching between the partial and full updates for PESC. This allows us to interpolate between versions of PESC that are efficient in terms of function evaluations and those that are efficient in terms of wall-clock time. Overall, we demonstrate that PESC is an effective algorithm that provides a promising direction towards a unified solution for constrained Bayesian optimization.Rafael del Pino Foundation, Google Focused Research Award, Engineering and Physical Sciences Research Council (Grant IDs: EP/I036575/1, EP/J012300/1

Lattice-gas simulations of Domain Growth, Saturation and Self-Assembly in Immiscible Fluids and Microemulsions

We investigate the dynamical behavior of both binary fluid and ternary microemulsion systems in two dimensions using a recently introduced hydrodynamic lattice-gas model of microemulsions. We find that the presence of amphiphile in our simulations reduces the usual oil-water interfacial tension in accord with experiment and consequently affects the non-equilibrium growth of oil and water domains. As the density of surfactant is increased we observe a crossover from the usual two-dimensional binary fluid scaling laws to a growth that is {\it slow}, and we find that this slow growth can be characterized by a logarithmic time scale. With sufficient surfactant in the system we observe that the domains cease to grow beyond a certain point and we find that this final characteristic domain size is inversely proportional to the interfacial surfactant concentration in the system.Comment: 28 pages, latex, embedded .eps figures, one figure is in colour, all in one uuencoded gzip compressed tar file, submitted to Physical Review

Counterion Condensation and Fluctuation-Induced Attraction

We consider an overall neutral system consisting of two similarly charged plates and their oppositely charged counterions and analyze the electrostatic interaction between the two surfaces beyond the mean-field Poisson-Boltzmann approximation. Our physical picture is based on the fluctuation-driven counterion condensation model, in which a fraction of the counterions is allowed to ``condense'' onto the charged plates. In addition, an expression for the pressure is derived, which includes fluctuation contributions of the whole system. We find that for sufficiently high surface charges, the distance at which the attraction, arising from charge fluctuations, starts to dominate can be large compared to the Gouy-Chapmann length. We also demonstrate that depending on the valency, the system may exhibit a novel first-order binding transition at short distances.Comment: 15 pages, 8 figures, to appear in PR

Partially Annealed Disorder and Collapse of Like-Charged Macroions

Charged systems with partially annealed charge disorder are investigated using field-theoretic and replica methods. Charge disorder is assumed to be confined to macroion surfaces surrounded by a cloud of mobile neutralizing counterions in an aqueous solvent. A general formalism is developed by assuming that the disorder is partially annealed (with purely annealed and purely quenched disorder included as special cases), i.e., we assume in general that the disorder undergoes a slow dynamics relative to fast-relaxing counterions making it possible thus to study the stationary-state properties of the system using methods similar to those available in equilibrium statistical mechanics. By focusing on the specific case of two planar surfaces of equal mean surface charge and disorder variance, it is shown that partial annealing of the quenched disorder leads to renormalization of the mean surface charge density and thus a reduction of the inter-plate repulsion on the mean-field or weak-coupling level. In the strong-coupling limit, charge disorder induces a long-range attraction resulting in a continuous disorder-driven collapse transition for the two surfaces as the disorder variance exceeds a threshold value. Disorder annealing further enhances the attraction and, in the limit of low screening, leads to a global attractive instability in the system.Comment: 21 pages, 2 figure

Screened non-bonded interactions in native proteins manipulate optimal paths for robust residue communication

A protein structure is represented as a network of residues whereby edges are determined by intra-molecular contacts. We introduce inhomogeneity into these networks by assigning each edge a weight that is determined by amino-acid pair potentials. Two methodologies are utilized to calculate the average path lengths (APLs) between pairs: To minimize (i) the maximum weight in the strong APL, and (ii) the total weight in the weak APL. We systematically screen edges that have higher than a cutoff potential and calculate the shortest APLs in these reduced networks, while keeping chain connectivity. Therefore, perturbations introduced at a selected region of the residue network propagate to remote regions only along the non-screened edges that retain their ability to disseminate the perturbation. The shortest APLs computed from the reduced homogeneous networks with only the strongest few non-bonded pairs closely reproduce the strong APLs from the weighted networks. The rate of change in the APL in the reduced residue network as compared to its randomly connected counterpart remains constant until a lower bound. Upon further link removal, this property shows an abrupt increase, towards a random coil behavior. Under different perturbation scenarios, diverse optimal paths emerge for robust residue communication.Comment: 21 pages with 6 figure

A Facile Strategy for In Situ Core-Template-Functionalizing Siliceous Hollow Nanospheres for Guest Species Entrapment

The shell wall-functionalized siliceous hollow nanospheres (SHNs) with functional molecules represent an important class of nanocarriers for a rich range of potential applications. Herein, a self-templated approach has been developed for the synthesis of in situ functionalized SHNs, in which the biocompatible long-chain polycarboxylates (i.e., polyacrylate, polyaspartate, gelatin) provide the framework for silica precursor deposition by simply controlling chain conformation with divalent metal ions (i.e., Ca2+, Sr2+), without the intervention of any external templates. Metal ions play crucial roles in the formation of organic vesicle templates by modulating the long chains of polymers and preventing them from separation by washing process. We also show that, by in situ functionalizing the shell wall of SHNs, it is capable of entrapping nearly an eightfold quantity of vitamin Bc in comparison to the bare bulk silica nanospheres. These results confirm the feasibility of guest species entrapment in the functionalized shell wall, and SHNs are effective carriers of guest (bio-)molecules potentially for a variety of biomedical applications. By rationally choosing the functional (self-templating) molecules, this concept may represent a general strategy for the production of functionalized silica hollow structures

Caprin Controls Follicle Stem Cell Fate in the Drosophila Ovary

Adult stem cells must balance self-renewal and differentiation for tissue homeostasis. The Drosophila ovary has provided a wealth of information about the extrinsic niche signals and intrinsic molecular processes required to ensure appropriate germline stem cell renewal and differentiation. The factors controlling behavior of the more recently identified follicle stem cells of the ovary are less well-understood but equally important for fertility. Here we report that translational regulators play a critical role in controlling these cells. Specifically, the translational regulator Caprin (Capr) is required in the follicle stem cell lineage to ensure maintenance of this stem cell population and proper encapsulation of developing germ cells by follicle stem cell progeny. In addition, reduction of one copy of the gene fmr1, encoding the translational regulator Fragile X Mental Retardation Protein, exacerbates the Capr encapsulation phenotype, suggesting Capr and fmr1 are regulating a common process. Caprin was previously characterized in vertebrates as Cytoplasmic Activation/Proliferation-Associated Protein. Significantly, we find that loss of Caprin alters the dynamics of the cell cycle, and we present evidence that misregulation of CycB contributes to the disruption in behavior of follicle stem cell progeny. Our findings support the idea that translational regulators may provide a conserved mechanism for oversight of developmentally critical cell cycles such as those in stem cell populations

Filament Depolymerization Can Explain Chromosome Pulling during Bacterial Mitosis

Chromosome segregation is fundamental to all cells, but the force-generating mechanisms underlying chromosome translocation in bacteria remain mysterious. Caulobacter crescentus utilizes a depolymerization-driven process in which a ParA protein structure elongates from the new cell pole, binds to a ParB-decorated chromosome, and then retracts via disassembly, pulling the chromosome across the cell. This poses the question of how a depolymerizing structure can robustly pull the chromosome that disassembles it. We perform Brownian dynamics simulations with a simple, physically consistent model of the ParABS system. The simulations suggest that the mechanism of translocation is “self-diffusiophoretic”: by disassembling ParA, ParB generates a ParA concentration gradient so that the ParA concentration is higher in front of the chromosome than behind it. Since the chromosome is attracted to ParA via ParB, it moves up the ParA gradient and across the cell. We find that translocation is most robust when ParB binds side-on to ParA filaments. In this case, robust translocation occurs over a wide parameter range and is controlled by a single dimensionless quantity: the product of the rate of ParA disassembly and a characteristic relaxation time of the chromosome. This time scale measures the time it takes for the chromosome to recover its average shape after it is has been pulled. Our results suggest explanations for observed phenomena such as segregation failure, filament-length-dependent translocation velocity, and chromosomal compaction