The optimization of functions to find the best solution according to one or several objectives has a central role in many engineering and research fields. Recently, a new family of optimization algorithms, named Quality-Diversity optimization, has been introduced, and contrasts with classic algorithms. Instead of searching for a single solution, Quality-Diversity algorithms are searching for a large collection of both diverse and high-performing solutions. The role of this collection is to cover the range of possible solution types as much as possible, and to contain the best solution for each type. The contribution of this paper is threefold. Firstly, we present a unifying framework of Quality-Diversity optimization algorithms that covers the two main algorithms of this family (Multi-dimensional Archive of Phenotypic Elites and the Novelty Search with Local Competition), and that highlights the large variety of variants that can be investigated within this family. Secondly, we propose algorithms with a new selection mechanism for Quality-Diversity algorithms that outperforms all the algorithms tested in this paper. Lastly, we present a new collection management that overcomes the erosion issues observed when using unstructured collections. These three contributions are supported by extensive experimental comparisons of Quality-Diversity algorithms on three different experimental scenarios.
In addition to direct applications, several other works focus on studying the properties of QD-algorithms. For example, @cite_35 revealed that extinction events (i.e., erasing a significant part of the collection) increases the evolvability of the solutions @cite_17 and allow the process to find higher-performing solutions afterwards. For example, with MAP-Elites, erasing the entire collection except 10 solutions every 100 000 generations increases the number of filled cells by $20 setups @cite_35 .
@cite_35 @cite_17
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There has been an increased growth in a number of applications that naturally generate large volumes of uncertain data. By the advent of such applications, the support of advanced analysis queries such as the skyline and its variant operators for big uncertain data has become important. In this paper, we propose the effective parallel algorithms using MapReduce to process the probabilistic skyline queries for uncertain data modeled by both discrete and continuous models. We present three filtering methods to identify probabilistic non-skyline objects in advance. We next develop a single MapReduce phase algorithm PS-QP-MR by utilizing space partitioning based on a variant of quadtrees to distribute the instances of objects effectively and the enhanced algorithm PS-QPF-MR by applying the three filtering methods additionally. We also propose the workload balancing technique to balance the workload of reduce functions based on the number of machines available. Finally, we present the brute-force algorithms PS-BR-MR and PS-BRF-MR with partitioning randomly and applying the filtering methods. In our experiments, we demonstrate the efficiency and scalability of PS-QPF-MR compared to the other algorithms. A challenge in evolutionary computation is to create representations as evolvable as those in natural evolution. This paper hypothesizes that extinction events, i.e. mass extinctions, can significantly increase evolvability, but only when combined with a divergent search algorithm, i.e. a search driven towards diversity (instead of optimality). Extinctions amplify diversity-generation by creating unpredictable evolutionary bottlenecks. Persisting through multiple such bottlenecks is more likely for lineages that diversify across many niches, resulting in indirect selection pressure for the capacity to evolve. This hypothesis is tested through experiments in two evolutionary robotics domains. The results show that combining extinction events with divergent search increases evolvability, while combining them with convergent search offers no similar benefit. The conclusion is that extinction events may provide a simple and effective mechanism to enhance performance of divergent search algorithms. While the covering algorithm has been perfected recently by the iterative approaches, such as DAOmap and IMap, its application has been limited to technology mapping. The main factor preventing the covering problem's migration to other logic transformations, such as elimination and resynthesis region identification found in SIS and FBDD, is the exponential number of alternative cuts that have to be evaluated. Traditional methods of cut generation do not scale beyond a cut size of 6. In this paper, a symbolic method that can enumerate all cuts is proposed without any pruning, up to a cut size of 10. We show that it can outperform traditional methods by an order of magnitude and, as a result, scales to 100K gate benchmarks. As a practical driver, the covering problem applied to elimination is shown where it can not only produce competitive area, but also provide more than 6times average runtime reduction of the total runtime in FBDD, a BDD based logic synthesis tool with a reported order of magnitude faster runtime than SIS and commercial tools with negligible impact on area. The Moran process, as studied by Lieberman, Hauert, and Nowak, is a randomised algorithm modelling the spread of genetic mutations in populations. The algorithm runs on an underlying graph where individuals correspond to vertices. Initially, one vertex (chosen uniformly at random) possesses a mutation, with fitness r > 1. All other individuals have fitness 1. During each step of the algorithm, an individual is chosen with probability proportional to its fitness, and its state (mutant or nonmutant) is passed on to an out-neighbour which is chosen uniformly at random. If the underlying graph is strongly connected, then the algorithm will eventually reach fixation, in which all individuals are mutants, or extinction, in which no individuals are mutants. An infinite family of directed graphs is said to be strongly amplifying if, for every r > 1, the extinction probability tends to 0 as the number of vertices increases. A formal definition is provided in the article. Strong amplification is a rather surprising property—it means that in such graphs, the fixation probability of a uniformly placed initial mutant tends to 1 even though the initial mutant only has a fixed selective advantage of r > 1 (independently of n). The name “strongly amplifying” comes from the fact that this selective advantage is “amplified.” Strong amplifiers have received quite a bit of attention, and proposed two potentially strongly amplifying families—superstars and metafunnels. Heuristic arguments have been published, arguing that there are infinite families of superstars that are strongly amplifying. The same has been claimed for metafunnels. In this article, we give the first rigorous proof that there is an infinite family of directed graphs that is strongly amplifying. We call the graphs in the family “megastars.” When the algorithm is run on an n-vertex graph in this family, starting with a uniformly chosen mutant, the extinction probability is roughly n − 1 2 (up to logarithmic factors). We prove that all infinite families of superstars and metafunnels have larger extinction probabilities (as a function of n). Finally, we prove that our analysis of megastars is fairly tight—there is no infinite family of megastars such that the Moran algorithm gives a smaller extinction probability (up to logarithmic factors). Also, we provide a counterexample which clarifies the literature concerning the isothermal theorem of The optimization of functions to find the best solution according to one or several objectives has a central role in many engineering and research fields. Recently, a new family of optimization algorithms, named quality-diversity (QD) optimization, has been introduced, and contrasts with classic algorithms. Instead of searching for a single solution, QD algorithms are searching for a large collection of both diverse and high-performing solutions. The role of this collection is to cover the range of possible solution types as much as possible, and to contain the best solution for each type. The contribution of this paper is threefold. First, we present a unifying framework of QD optimization algorithms that covers the two main algorithms of this family (multidimensional archive of phenotypic elites and the novelty search with local competition), and that highlights the large variety of variants that can be investigated within this family. Second, we propose algorithms with a new selection mechanism for QD algorithms that outperforms all the algorithms tested in this paper. Lastly, we present a new collection management that overcomes the erosion issues observed when using unstructured collections. These three contributions are supported by extensive experimental comparisons of QD algorithms on three different experimental scenarios. We consider the task of enumerating and counting answers to k-ary conjunctive queries against relational databases that may be updated by inserting or deleting tuples. We exhibit a new notion of q-hierarchical conjunctive queries and show that these can be maintained efficiently in the following sense. During a linear time pre-processing phase, we can build a data structure that enables constant delay enumeration of the query results; and when the database is updated, we can update the data structure and restart the enumeration phase within constant time. For the special case of self-join free conjunctive queries we obtain a dichotomy: if a query is not q-hierarchical, then query enumeration with sublinear *) delay and sublinear update time (and arbitrary preprocessing time) is impossible. For answering Boolean conjunctive queries and for the more general problem of counting the number of solutions of k-ary queries we obtain complete dichotomies: if the query's homomorphic core is q-hierarchical, then size of the the query result can be computed in linear time and maintained with constant update time. Otherwise, the size of the query result cannot be maintained with sublinear update time. All our lower bounds rely on the OMv-conjecture, a conjecture on the hardness of online matrix-vector multiplication that has recently emerged in the field of fine-grained complexity to characterise the hardness of dynamic problems. The lower bound for the counting problem additionally relies on the orthogonal vectors conjecture, which in turn is implied by the strong exponential time hypothesis.*) By sublinear we mean O(n(1-e) for some e > 0, where n is the size of the active domain of the current database. This paper presents a new approach to hierarchical reinforcement learning based on decomposing the target Markov decision process (MDP) into a hierarchy of smaller MDPs and decomposing the value function of the target MDP into an additive combination of the value functions of the smaller MDPs. The decomposition, known as the MAXQ decomposition, has both a procedural semantics--as a subroutine hierarchy--and a declarative semantics--as a representation of the value function of a hierarchical policy. MAXQ unifies and extends previous work on hierarchical reinforcement learning by Singh, Kaelbling, and Dayan and Hinton. It is based on the assumption that the programmer can identify useful subgoals and define subtasks that achieve these subgoals. By defining such subgoals, the programmer constrains the set of policies that need to be considered during reinforcement learning. The MAXQ value function decomposition can represent the value function of any policy that is consistent with the given hierarchy. The decomposition also creates opportunities to exploit state abstractions, so that individual MDPs within the hierarchy can ignore large parts of the state space. This is important for the practical application of the method. This paper defines the MAXQ hierarchy, proves formal results on its representational power, and establishes five conditions for the safe use of state abstractions. The paper presents an online model-free learning algorithm, MAXQ-Q, and proves that it converges with probability 1 to a kind of locally-optimal policy known as a recursively optimal policy, even in the presence of the five kinds of state abstraction. The paper evaluates the MAXQ representation and MAXQ-Q through a series of experiments in three domains and shows experimentally that MAXQ-Q (with state abstractions) converges to a recursively optimal policy much faster than flat Q learning. The fact that MAXQ learns a representation of the value function has an important benefit: it makes it possible to compute and execute an improved, non-hierarchical policy via a procedure similar to the policy improvement step of policy iteration. The paper demonstrates the effectiveness of this nonhierarchical execution experimentally. Finally, the paper concludes with a comparison to related work and a discussion of the design tradeoffs in hierarchical reinforcement learning. Cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity, see, e.g., B. Kerr, M. A. Riley, M. W. Feldman and B. J. M. Bohannan Nature 418, 171 (2002)] and B. Kirkup and M. A. Riley Nature 428, 412 (2004)]. Through analytical methods supported by numerical simulations, we address this issue by studying the properties of a paradigmatic non-spatial three-species stochastic system, namely, the "rock-paper-scissors" or cyclic Lotka-Volterra model. While the deterministic approach (rate equations) predicts the coexistence of the species resulting in regular (yet neutrally stable) oscillations of the population densities, we demonstrate that fluctuations arising in the system with a finite number of agents drastically alter this picture and are responsible for extinction: After long enough time, two of the three species die out. As main findings we provide analytic estimates and numerical computation of the extinction probability at a given time. We also discuss the implications of our results for a broad class of competing population systems. This paper presents a novel evolutionary optimization strategy based on the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). This new approach is intended to reduce the number of generations required for convergence to the optimum. Reducing the number of generations, i.e., the time complexity of the algorithm, is important if a large population size is desired: (1) to reduce the effect of noise; (2) to improve global search properties; and (3) to implement the algorithm on (highly) parallel machines. Our method results in a highly parallel algorithm which scales favorably with large numbers of processors. This is accomplished by efficiently incorporating the available information from a large population, thus significantly reducing the number of generations needed to adapt the covariance matrix. The original version of the CMA-ES was designed to reliably adapt the covariance matrix in small populations but it cannot exploit large populations efficiently. Our modifications scale up the efficiency to population sizes of up to 10n, where n is the problem dimension. This method has been applied to a large number of test problems, demonstrating that in many cases the CMA-ES can be advanced from quadratic to linear time complexity. Topic models, such as Latent Dirichlet Allocation (LDA), posit that documents are drawn from admixtures of distributions over words, known as topics. The inference problem of recovering topics from admixtures, is NP-hard. Assuming separability, a strong assumption, [4] gave the first provable algorithm for inference. For LDA model, [6] gave a provable algorithm using tensor-methods. But [4,6] do not learn topic vectors with bounded @math error (a natural measure for probability vectors). Our aim is to develop a model which makes intuitive and empirically supported assumptions and to design an algorithm with natural, simple components such as SVD, which provably solves the inference problem for the model with bounded @math error. A topic in LDA and other models is essentially characterized by a group of co-occurring words. Motivated by this, we introduce topic specific Catchwords, group of words which occur with strictly greater frequency in a topic than any other topic individually and are required to have high frequency together rather than individually. A major contribution of the paper is to show that under this more realistic assumption, which is empirically verified on real corpora, a singular value decomposition (SVD) based algorithm with a crucial pre-processing step of thresholding, can provably recover the topics from a collection of documents drawn from Dominant admixtures. Dominant admixtures are convex combination of distributions in which one distribution has a significantly higher contribution than others. Apart from the simplicity of the algorithm, the sample complexity has near optimal dependence on @math , the lowest probability that a topic is dominant, and is better than [4]. Empirical evidence shows that on several real world corpora, both Catchwords and Dominant admixture assumptions hold and the proposed algorithm substantially outperforms the state of the art [5]. This paper presents two techniques for improving garbage collection performance: generational stack collection and profile-driven pretenuring. The first is applicable to stack-based implementations of functional languages while the second is useful for any generational collector. We have implemented both techniques in a generational collector used by the TIL compiler (Tarditi, Morrisett, Cheng, Stone, Harper, and Lee 1996), and have observed decreases in garbage collection times of as much as 70 and 30 , respectively.Functional languages encourage the use of recursion which can lead to a long chain of activation records. When a collection occurs, these activation records must be scanned for roots. We show that scanning many activation records can take so long as to become the dominant cost of garbage collection. However, most deep stacks unwind very infrequently, so most of the root information obtained from the stack remains unchanged across successive garbage collections. Generational stack collection greatly reduces the stack scan cost by reusing information from previous scans.Generational techniques have been successful in reducing the cost of garbage collection (Ungar 1984). Various complex heap arrangements and tenuring policies have been proposed to increase the effectiveness of generational techniques by reducing the cost and frequency of scanning and copying. In contrast, we show that by using profile information to make lifetime predictions, pretenuring can avoid copying data altogether. In essence, this technique uses a refinement of the generational hypothesis (most data die young) with a locality principle concerning the age of data: most allocations sites produce data that immediately dies, while a few allocation sites consistently produce data that survives many collections. An edge-Markovian process with birth-rate p and death-rate q generates sequences of graphs (G0,G1,G2,…) with the same node set [n] such that Gt is obtained from Gt−1 as follows: if e ∉ E(Gt−1) then e ∈ E(Gt) with probability p, and if e ∈ E(Gt−1) then e ∉ E(Gt) with probability q. (PODC 2008) analyzed thoroughly information dissemination in such dynamic graphs, by establishing bounds on their flooding time--flooding is the basic mechanism in which every node becoming aware of an information at step t forwards this information to all its neighbors at all forthcoming steps t∦ > t. In this paper, we establish tight bounds on the complexity of flooding for all possible birth rates and death rates, completing the previous results by Moreover, we note that despite its many advantages in term of simplicity and robustness, flooding suffers from its high bandwidth consumption. Hence we also show that flooding in dynamic graphs can be implemented in a more parsimonious manner, so that to save bandwidth, yet preserving efficiency in term of simplicity and completion time. For a positive integer k, we say that the flooding protocol is k-active if each node forwards an information only during the k time steps immediately following the step at which the node receives that information for the first time. We define the reachability threshold for the flooding protocol as the smallest integer k such that, for any source s ∈ [n], the k-active flooding protocol from s completes (i.e., reaches all nodes), and we establish tight bounds for this parameter. We show that, for a large spectrum of parameters p and q, the reachability threshold is by several orders of magnitude smaller than the flooding time. In particular, we show that it is even constant whenever the ratio p (p + q) exceeds log n n. Moreover, we also show that being active for a number of steps equal to the reachability threshold (up to a multiplicative constant) allows the flooding protocol to complete in optimal time, i.e., in asymptotically the same number of steps as when being perpetually active. These results demonstrate that flooding can be implemented in a practical and efficient manner in dynamic graphs. The main ingredient in the proofs of our results is a reduction lemma enabling to overcome the time dependencies in edge-Markovian dynamic graphs. Many fields use search algorithms, which automatically explore a search space to find high-performing solutions: chemists search through the space of molecules to discover new drugs; engineers search for stronger, cheaper, safer designs, scientists search for models that best explain data, etc. The goal of search algorithms has traditionally been to return the single highest-performing solution in a search space. Here we describe a new, fundamentally different type of algorithm that is more useful because it provides a holistic view of how high-performing solutions are distributed throughout a search space. It creates a map of high-performing solutions at each point in a space defined by dimensions of variation that a user gets to choose. This Multi-dimensional Archive of Phenotypic Elites (MAP-Elites) algorithm illuminates search spaces, allowing researchers to understand how interesting attributes of solutions combine to affect performance, either positively or, equally of interest, negatively. For example, a drug company may wish to understand how performance changes as the size of molecules and their cost-to-produce vary. MAP-Elites produces a large diversity of high-performing, yet qualitatively different solutions, which can be more helpful than a single, high-performing solution. Interestingly, because MAP-Elites explores more of the search space, it also tends to find a better overall solution than state-of-the-art search algorithms. We demonstrate the benefits of this new algorithm in three different problem domains ranging from producing modular neural networks to designing simulated and real soft robots. Because MAP- Elites (1) illuminates the relationship between performance and dimensions of interest in solutions, (2) returns a set of high-performing, yet diverse solutions, and (3) improves finding a single, best solution, it will advance science and engineering. Mutation operators such as Gaussian, Levy and Cauchy have been used with evolutionary programming (EP). According to the no free lunch theorem, it is impossible for EP with a single mutation operator to outperform always. For example, Classical EP (CEP) with Gaussian mutation is better at searching in a local neighborhood while the Fast EP (FEP) with the Cauchy mutation performs better over a larger neighborhood. Motivated by these observations, we propose an ensemble approach where each mutation operator has its associated population and every population benefits from every function call. This approach enables us to benefit from different mutation operators with different parameter values whenever they are effective during different stages of the search process. In addition, the recently proposed Adaptive EP (AEP) using Gaussian (ACEP) and Cauchy (AFEP) mutations is also evaluated. In the AEP, the strategy parameter values are adapted based on the search performance in the previous few generations. The performance of ensemble is compared with a mixed mutation strategy, which integrates several mutation operators into a single algorithm as well as against the AEP with a single mutation operator. Improved performance of the ensemble over the single mutation-based algorithms and mixed mutation algorithm is verified using statistical tests. 0. Background Notes.- 1. Continuous Partitions of Unity.- 2. Absolutely Continuous Functions.- 3. Some Compactness Theorems.- 4. Weak Convergence and Asymptotic Center of Bounded Sequences.- 5. Closed Convex Hulls and the Mean-Value Theorem.- 6. Lower Semicontinuous Convex Functions and Projections of Best Approximation.- 7. A Concise Introduction to Convex Analysis.- 1. Set-Valued Maps.- 1. Set-Valued Maps and Continuity Concepts.- 2. Examples of Set-Valued Maps.- 3. Continuity Properties of Maps with Closed Convex Graph.- 4. Upper Hemicontinuous Maps and the Convergence Theorem.- 5. Hausdorff Topology.- 6. The Selection Problem.- 7. The Minimal Selection.- 8. Chebishev Selection.- 9. The Barycentric Selection.- 10. Selection Theorems for Locally Selectionable Maps.- 11. Michael's Selection Theorem.- 12. The Approximate Selection Theorem and Kakutani's Fixed Point Theorem.- 13. (7-Selectionable Maps.- 14. Measurable Selections.- 2. Existence of Solutions to Differential Inclusions.- 1. Convex Valued Differential Inclusions.- 2. Qualitative Properties of the Set of Trajectories of Convex-Valued Differential Inclusions.- 3. Nonconvex-Valued Differential Inclusions.- 4. Differential Inclusions with Lipschitzean Maps and the Relaxation Theorem.- 5. The Fixed-Point Approach.- 6. The Lower Semicontinuous Case.- 3. Differential Inclusions with Maximal Monotone Maps.- 1. Maximal Monotone Maps.- 2. Existence and Uniqueness of Solutions to Differential Inclusions with Maximal Monotone Maps.- 3. Asymptotic Behavior of Trajectories and the Ergodic Theorem.- 4. Gradient Inclusions.- 5. Application: Gradient Methods for Constrained Minimization Problems.- 4. Viability Theory: The Nonconvex Case.- 1. Bouligand's Contingent Cone.- 2. Viable and Monotone Trajectories.- 3. Contingent Derivative of a Set-Valued Map.- 4. The Time Dependent Case.- 5. A Continuous Version of Newton's Method.- 6. A Viability Theorem for Continuous Maps with Nonconvex Images..- 7. Differential Inclusions with Memory.- 5. Viability Theory and Regulation of Controled Systems: The Convex Case.- 1. Tangent Cones and Normal Cones to Convex Sets.- 2. Viability Implies the Existence of an Equilibrium.- 3. Viability Implies the Existence of Periodic Trajectories.- 4. Regulation of Controled Systems Through Viability.- 5. Walras Equilibria and Dynamical Price Decentralization.- 6. Differential Variational Inequalities.- 7. Rate Equations and Inclusions.- 6. Liapunov Functions.- 1. Upper Contingent Derivative of a Real-Valued Function.- 2. Liapunov Functions and Existence of Equilibria.- 3. Monotone Trajectories of a Differential Inclusion.- 4. Construction of Liapunov Functions.- 5. Stability and Asymptotic Behavior of Trajectories.- Comments. While evolutionary computation and evolutionary robotics take inspiration from nature, they have long focused mainly on problems of performance optimization. Yet evolution in nature can be interpreted as more nuanced than a process of simple optimization. In particular, natural evolution is a divergent search that optimizes locally within each niche as it simultaneously diversifies. This tendency to discover both quality and diversity at the same time differs from many of the conventional algorithms of machine learning, and also thereby suggests a different foundation for inferring the approach of greatest potential for evolutionary algorithms. In fact, several recent evolutionary algorithms called quality diversity (QD) algorithms(e.g. novelty search with local competition and MAP-Elites) have drawn inspiration from this more nuanced view, aiming to fill a space of possibilities with the best possible example of each type of achievable behavior. The result is a new class of algorithms that return an archive of diverse, high-quality behaviors in a single run. The aim in this paper is to study the application of QD algorithms in challenging environments (in particular complex mazes) to establish their best practices for ambitious domains in the future. In addition to providing insight into cases when QD succeeds and fails, a new approach is investigated that hybridizes multiple views of behaviors (called behavior characterizations) in the same run, which succeeds in overcoming some of the challenges associated with searching for QD with respect to a behavior characterization that is not necessarily sufficient for generating both quality and diversity at the same time. Harvesting relational facts from Web sources has received great attention for automatically constructing large knowledge bases. Stateof-the-art approaches combine pattern-based gathering of fact candidates with constraint-based reasoning. However, they still face major challenges regarding the trade-offs between precision, recall, and scalability. Techniques that scale well are susceptible to noisy patterns that degrade precision, while techniques that employ deep reasoning for high precision cannot cope with Web-scale data. This paper presents a scalable system, called PROSPERA, for high-quality knowledge harvesting. We propose a new notion of ngram-itemsets for richer patterns, and use MaxSat-based constraint reasoning on both the quality of patterns and the validity of fact candidates.We compute pattern-occurrence statistics for two benefits: they serve to prune the hypotheses space and to derive informative weights of clauses for the reasoner. The paper shows how to incorporate these building blocks into a scalable architecture that can parallelize all phases on a Hadoop-based distributed platform. Our experiments with the ClueWeb09 corpus include comparisons to the recent ReadTheWeb experiment. We substantially outperform these prior results in terms of recall, with the same precision, while having low run-times. Sequence generative adversarial networks (SeqGAN) have been used to improve conditional sequence generation tasks, for example, chit-chat dialogue generation. To stabilize the training of SeqGAN, Monte Carlo tree search (MCTS) or reward at every generation step (REGS) is used to evaluate the goodness of a generated subsequence. MCTS is computationally intensive, but the performance of REGS is worse than MCTS. In this paper, we propose stepwise GAN (StepGAN), in which the discriminator is modified to automatically assign scores quantifying the goodness of each subsequence at every generation step. StepGAN has significantly less computational costs than MCTS. We demonstrate that StepGAN outperforms previous GAN-based methods on both synthetic experiment and chit-chat dialogue generation. Many state-of-the-art garbage collectors are generational, collecting the young nursery objects more frequently than old objects. These collectors perform well because young objects tend to die at a higher rate than old ones. However, these collectors do not examine object lifetimes with respect to any particular program or allocation site. This paper introduces low-cost object sampling to dynamically determine lifetimes. The sampler marks an object and records its allocation site every n bytes of allocation. The collector then computes per-site nursery survival rates. Sampling degrades total performance by only 3 on average for sample rates of 256 bytes in jikes, a rate at which overall lifetime accuracy compares well with sampling every object. An adaptive collector can use this information to tune itself. For example, pretenuring decreases nursery collection work by allocating new, but long-lived, objects directly into the mature space. We introduce a dynamic pretenuring mechanism that detects long lived allocation sites and pretenures them, given sufficient samples. To react to phase changes, it occasionally backsamples. As with previous online pretenuring, consistent performance improvements on SPECjvm98 benchmarks are difficult to attain since only two combine sufficient allocation load with high nursery survival. Our pretenuring system consistently improves one of these, javac, by 2 to 9 of total time by decreasing collection time by over a factor of two. Sampling and pretenuring overheads slow down all the others. This paper thus provides an efficient sampling mechanism that accurately predicts lifetimes, but leaves open optimization policies that can exploit this information. We introduce a new technique that can reduce any higher-order Markov random field with binary labels into a first-order one that has the same minima as the original. Moreover, we combine the reduction with the fusion-move and QPBO algorithms to optimize higher-order multi-label problems. While many vision problems today are formulated as energy minimization problems, they have mostly been limited to using first-order energies, which consist of unary and pairwise clique potentials, with a few exceptions that consider triples. This is because of the lack of efficient algorithms to optimize energies with higher-order interactions. Our algorithm challenges this restriction that limits the representational power of the models, so that higher-order energies can be used to capture the rich statistics of natural scenes. To demonstrate the algorithm, we minimize a third-order energy, which allows clique potentials with up to four pixels, in an image restoration problem. The problem uses the fields of experts model, a learned spatial prior of natural images that has been used to test two belief propagation algorithms capable of optimizing higher-order energies. The results show that the algorithm exceeds the BP algorithms in both optimization performance and speed.