We propose computer-assisted techniques for helping with pedagogy in Algebra. In particular, given a proof problem p (of the form “Left-hand-side-term = Right-hand-side-term”), we show how to automatically generate problems that are similar to p. We believe that such a tool can be used by teachers in making examinations where they need to test students on problems similar to what they taught in class, and by students in generating practice problems tailored to their specific needs. Our first insight is that we can generalize p syntactically to a query Q that implicitly represents a set of problems [[Q]] (which includes p). Our second insight is that we can explore the space of problems [[Q]] automatically, use classical results from polynomial identity testing to generate only those problems in [[Q]] that are correct, and then use pruning techniques to generate only unique and interesting problems. Our third insight is that with a small amount of manual tuning on the query Q, the user can interactively guide the computer to generate problems of interest to her. We present the technical details of the above mentioned steps, and also describe a tool where these steps have been implemented. We also present an empirical evaluation on a wide variety of problems from various sub-fields of algebra including polynomials, trigonometry, calculus, determinants etc. Our tool is able to generate a rich corpus of similar problems from each given problem; while some of these similar problems were already present in the textbook, several were new!

Modeling visual saliency map of an image provides important information for image semantic understanding in many applications. Most existing computational visual saliency models follow a bottom-up framework that generates independent saliency map in each selected visual feature space and combines them in a proper way. Two big challenges to be addressed explicitly in these methods are (1) which features should be extracted for all pixels of the input image and (2) how to dynamically determine importance of the saliency map generated in each feature space. In order to address these problems, we present a novel saliency map computational model based on tensor decomposition and reconstruction. Tensor representation and analysis not only explicitly represent image's color values but also imply two important relationships inherent to color image. One is reflecting spatial correlations between pixels and the other one is representing interplay between color channels. Therefore, saliency map generator based on the proposed model can adaptively find the most suitable features and their combinational coefficients for each pixel. Experiments on a synthetic image set and a real image set show that our method is superior or comparable to other prevailing saliency map models.

Problem-solving procedures have been typically aimed at achieving well-defined goals or satisfying straightforward preferences. However, learners and solvers may often generate rich multiattribute results with procedures guided by sets of controls that define different dimensions of quality. We explore methods that enable people to explore and express preferences about the operation of classification models in supervised multiclass learning. We leverage a leave-one-out confusion matrix that provides users with views and real-time controls of a model space. The approach allows people to consider in an interactive manner the global implications of local changes in decision boundaries. We focus on kernel classifiers and show the effectiveness of the methodology on a variety of tasks.

The production of any new medicine requires solutions to many planning problems. The most fundamental of these is determining the sequence of chemical reactions necessary to physically create the drug. Surprisingly, these organic syntheses can be modeled as branching paths in a discrete, fully-observable state space, making the construction of new medicines an application of heuristic search. We describe a model of organic chemistry that is amenable to traditional AI techniques from game tree search, regression, and automatic assembly sequencing. We demonstrate the applicability of AND/OR graph search by developing the first chemistry solver to use proof-number search. Finally, we construct a benchmark suite of organic synthesis problems collected from undergraduate organic chemistry exams, and we analyze our solvers performance both on this suite and in recreating the synthetic plan for a multibillion dollar drug.

Coordination in mixed agent-human environments is an important, yet not a simple, problem. Little attention has been given to the issues raised in teams that consist of both computerized agents and people. In such situations different considerations are in order, as people tend to make mistakes and they are affected by cognitive, social and cultural factors. In this paper we present a novel agent designed to proficiently coordinate with a human counterpart. The agent uses a neural network model that is based on a pre-existing knowledge base which allows it to achieve an efficient modeling of a human's decisions and predict their behavior. A novel communication mechanism which takes into account the expected effect of communication on the other member will allow communication costs to be minimized. In extensive simulations involving more than 200 people we investigated our approach and showed that our agent achieves better coordination when involved, compared to settings in which only humans or another state-of-the-art agent are involved.

General Game Playing (GGP) agents must be capable of playing a wide variety of games skillfully. Monte-Carlo Tree Search (MCTS) has proven an effective reasoning mechanism for this challenge, as is reflected by its popularity among designers of GGP agents. Providing GGP agents with the knowledge relevant to the game at hand in real time is, however, a challenging task. In this paper we propose two enhancements for MCTS in the context of GGP, aimed at improving the effectiveness of the simulations in real time based on in-game statistical feedback. The first extension allows early termination of lengthy and uninformative simulations while the second improves the action-selection strategy when both explored and unexplored actions are available. The methods are empirically evaluated in a state-of-the-art GGP agent and shown to yield an overall significant improvement in playing strength.

The core is a central solution concept in cooperative game theory, and therefore it is important to know under what conditions the core of a game is guaranteed to be non-empty. Two notions that prove to be very useful in this context are Linear Programming (LP) duality and convexity. In this work, we apply these tools to identify games with overlapping coalitions (OCF games) that admit stable outcomes. We focus on three notions of the core defined in (Chalkiadakis et al. 2010) for such games, namely, the conservative core, the refined core and the optimistic core. First, we show that the conservative core of an OCF game is non-empty if and only if the core of a related classic coalitional game is non-empty. This enables us to improve the result of (Chalkiadakis et al. 2010) by giving a strictly weaker sufficient condition for the non-emptiness of the conservative core. We then use LP duality to characterize OCF games with non-empty refined core; as a corollary, we show that the refined core of a game is non-empty as long as the superadditive cover of its characteristic function is convex. Finally, we identify a large class of OCF games that can be shown to have a non-empty optimistic core using an LP based argument.

This research is motivated by large scale problems in urban transportation and labor mobility where there is congestion for resources and uncertainty in movement. In such domains, even though the individual agents do not have an identity of their own and do not explicitly interact with other agents, they effect other agents. While there has been much research in handling such implicit effects, it has primarily assumed de- terministic movements of agents. We address the issue of decision support for individual agents that are identical and have involuntary movements in dynamic environments. For instance, in a taxi fleet serving a city, when a taxi is hired by a customer, its movements are uncontrolled and depend on (a) the customers requirement; and (b) the location of other taxis in the fleet. Towards addressing decision support in such problems, we make two key contributions: (a) A framework to represent the decision problem for selfish individuals in a dynamic population, where there is transitional uncertainty (involuntary movements); and (b) Two techniques (Fictitious Play for Symmetric Agent Populations, FP-SAP and Soft- max based Flow Update, SMFU) that converge to equilibrium solutions. We show that our techniques (apart from providing equilibrium strategies) outperform “driver” strategies with re- spect to overall availability of taxis and the revenue obtained by the taxi drivers. We demonstrate this on a real world data set with 8,000 taxis and 83 zones (representing the entire area of Singapore).

Many strategic actions carry a ‘contagious’ component beyond the immediate locale of the effort itself. Viral marketing and peacekeeping operations have both been observed to have a spreading effect. In this work, we use counterinsurgency as our illustrative domain. Defined as the effort to block the spread of support for an insurgency, such operations lack the manpower to defend the entire population and must focus onthe opinions of a subset of local leaders. As past researchers of security resource allocation have done, we propose using game theory to develop such policies and model the interconnected network of leaders as a graph. Unlike this past work in security games, actions in these domains possess a probabilistic, non-local impact. To address this new class of security games, we combine recent research in influence blocking maximization with a double oracle approach and create novel heuristic oracles to generate mixed strategies for a real-world leadership network from Afghanistan, synthetic leadership networks, and a real social network. We find that leadership networks that exhibit highly interconnected clusters can be solved equally well by our heuristic methods, but our more sophisticated heuristics outperform simpler ones in less interconnected social networks.

Designing revenue-optimal auctions for various settings is perhaps the most important, yet sometimes most elusive, problem in mechanism design. Spiteful bidders have been intensely studied recently, especially because spite occurs in many applications in multiagent system and electronic commerce. We derive the optimal auction for such bidders (as well as bidders that are altruistic). It is a generalization of Myerson’s (1981) auction. It chooses an allocation that maximizes agents’ virtual valuations, but for a generalized definition of virtual valuation. The payment rule is less intuitive. For one, it takes each bidder’s own report into consideration when determining his payment. Moreover, bidders pay even if the seller keeps the item; a similar phenomenon has been shown in other settings with neg- ative externalities (Jehiel, Moldovanu, and Stacchetti 1996; Deng and Pekec 2011). On the other hand, a novel aspect of our auction is that it sometimes subsidizes losers when the item is sold to some other bidder. We also derive a revenue equivalence theorem for this setting. Using it, we generate a short proof of (a slight generalization of) the previously known result that, in two-bidder settings with independently uniformly drawn valuations, second-price auctions yield greater expected revenue than first-price auctions. Finally, we present a template for comparing the expected revenues of any two auction mechanisms that have the same allocation rule (for the valuations distributions at hand).