Simple examples are teaching treasures. Finding a concise, effective illustration is like finding a precious gem. When such an example is fun and intriguing, it is educational gold. In this paper, we share the jeopardy dice game of Pig, which has extremely simple rules, engaging play, and a complex optimal policy. We describe its historical uses in mathematics, and share ways in which we have used the game to teach basic concepts in CS1, and intermediate concepts in introductory artificial intelligence, networking, and scientific visualization courses. We also describe the rich challenges Pig offers for undergraduate research in machine learning.

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Abstract. In this paper, we demonstrate the ease in which an adaptive simulated annealing algorithm can be designed. Specifically, we use the adaptive annealing schedule known as the modified Lam schedule to apply simulated annealing to the weighted tardiness scheduling problem with sequence-dependent setups. The modified Lam annealing schedule adjusts the temperature to track the theoretical optimal rate of accepted moves. Employing the modified Lam schedule allows us to avoid the often tedious tuning of the annealing schedule; as the algorithm tunes itself for each instance during problem solving. Our results show that an adaptive simulated annealer can be competitive when compared to highly tuned, hand crafted algorithms. Specifically, we compare our results to a state-of-theart genetic algorithm for weighted tardiness scheduling with sequence-dependent setups. Our study serves as an illustration of the ease with which a parameter-free simulated annealer can be designed and implemented. 1

Boggle is a fast-paced word search game played on a five-by-five grid of letters. To remove any trace of fun from the game, I have conducted an extensive analysis of Boggle, using a newly-constructed software tool. I present the tool and the Boggle insights it provides. 1

The most significant impediment for protein structure prediction is the inadequacy of conformation space search methods. Conformation space is too large and the energy landscape too rugged for existing search methods to consistently find near-optimal minima. To alleviate this problem, we present model-based search, a novel conformation space search method. Model-based search uses highly accurate information obtained during search to build an approximate, partial model of the energy landscape. Model-based search aggregates information in the model as it progresses, and in turn uses this information to guide exploration towards regions most likely to contain a near-optimal minimum. We validate our method by predicting the structure of 32 proteins, ranging in length from 49 to 213 amino acids. Our results demonstrate that model-based search is more effective at finding lowenergy conformations in high-dimensional conformation spaces than existing search methods. The lower-energy conformations found by our method also correspond to higher-accuracy structure predictions. 1

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This paper describes Stage, a learning algorithm that automatically improves search performance on large-scale optimization problems. Stage learns an evaluation function that predicts the outcome of a local search algorithm, such as hillclimbing or Walksat, from features of states visited during search. The learned evaluation function is used to bias future search trajectories toward better optima on the same problem. This paper presents the Stage algorithm; an extension, X-Stage, that transfers learned evaluation functions to new, similar optimization problems; and empirical results on seven large-scale optimization domains: bin-packing, channel routing, Bayes network structure-finding, radiotherapy treatment planning, cartogram design, Boolean satisfiability, and Boggle board setup.

The choice of a good annealing schedule is necessary for good performance of simulated annealing for combinatorial optimization problems. In this paper, we pose the simulated annealing task decision-theoretically for the first time, allowing the user to explicitly define utilities of time and solution quality. We then demonstrate the application of reinforcement learning techniques towards approximately optimal annealing control, using traveling salesman, clustered traveling salesman, and scheduling problems. Although many means of automating control of annealing temperatures have been proposed, our techniques requires no domain-specific knowledge of problems and provides a natural means of expressing time versus quality tradeoffs. Finally, we discuss alternate abstractions for future decision-theoretic variants.

Keywords:Protein structure prediction, conformational space search, multiple energy functions, active learning, Rosetta, Monte Carlo. The most significant impediment for protein structure prediction is the inadequacy of conformation space search. Conformation space is too large and the energy landscape too rugged for existing search methods to consistently find near-optimal minima. To alleviate this problem, we present model-based search, a novel conformation space search method. Model-based search uses highly accurate information obtained during search to build an approximate, partial model of the energy landscape. Modelbased search aggregates information in the model as it progresses, and in turn uses this information to guide exploration towards regions most likely to contain a nearoptimal minimum. We validate our method by predicting the structure of 32 proteins, ranging in length from 49 to 213 amino acids. Our results demonstrate that modelbased search is more effective at finding low-energy conformations in high-dimensional conformation spaces than existing search methods. The reduction in energy translates into structure predictions of increased accuracy. 1

In complex real-world environments, traditional (tabular) techniques for solving Reinforcement Learning (RL) do not scale. Function approximation is needed, but unfortunately, existing approaches generally have poor convergence and optimality guarantees. Additionally, for the case of human environments, it is valuable to be able to leverage human input. In this paper we introduce Expanding Value Function Approximation (EVFA), a function approximation algorithm that returns the optimal value function given sufficient rounds. To leverage human input, we introduce a new human-agent interaction scheme, training regimens, which allow humans to interact with and improve agent learning in the setting of a machine learning game. In experiments, we show EVFA compares favorably to standard value approximation approaches. We also show that training regimens enable humans to further improve EVFA performance. In our user study, we find that non-experts are able to provide effective regimens and that they found the game fun. Categories and Subject Descriptors