We address the problem of image hashing by learning binary codes from large and weakly supervised photo collections. Due to the explosive growth of user generated media on the Web, this problem is becoming critical for large-scale visual applications like image retrieval. While most existing hashing methods fail to address this challenge well, our method shows promising improvement due to the following two key advantages.First, we formulate a novel hashing objective that can effectively mine implicit weak supervision by collaborative filtering. Second, we propose a discrete hashing algorithm, offered with efficient optimization, to overcome the inferior optimizations in obtaining binary codes from real-valued solutions. In this way, our method can be considered as a weakly-supervised discrete hashing framework which jointly learns image semantics and their corresponding binary codes. Through training on one million weakly annotated images, our experimental results demonstrate that image retrieval using the proposed hashing method outperforms the other state-of-the-art ones on image and video benchmarks.

Semi-definite rank minimization problems model a wide range of applications in both signal processing and machine learning fields. This class of problem is NP-hard in general. In this paper, we propose a proximal Alternating Direction Method (ADM) for the well-known semi-definite rank regularized minimization problem. Specifically, we first reformulate this NP-hard problem as an equivalent biconvex MPEC (Mathematical Program with Equilibrium Constraints), and then solve it using proximal ADM, which involves solving a sequence of structured convex semi-definite subproblems to find a desirable solution to the original rank regularized optimization problem. Moreover, based on the Kurdyka-Lojasiewicz inequality, we prove that the proposed method always converges to a KKT stationary point under mild conditions. We apply the proposed method to the widely studied and popular sensor network localization problem. Our extensive experiments demonstrate that the proposed algorithm outperforms state-of-the-art low-rank semi-definite minimization algorithms in terms of solution quality.

Large-scale Nuclear Norm penalized Least Square problem (NNLS) is frequently encountered in estimation of low rank structures. In this paper we accelerate the solution procedure by combining non-smooth convex optimization with smooth Riemannian method. Our methods comprise of two phases. In the first phase, we use Alternating Direction Method of Multipliers (ADMM) both to identify the fix rank manifold where an optimum resides and to provide an initializer for the subsequent refinement. In the second phase, two superlinearly convergent Riemannian methods: Riemannian NewTon (NT) and Riemannian Conjugate Gradient descent (CG) are adopted to improve the approximation over a fix rank manifold. We prove that our Hybrid method of ADMM and NT (HADMNT) converges to an optimum of NNLS at least quadratically. The experiments on large-scale collaborative filtering datasets demonstrate very competitive performance of these fast hybrid methods compared to the state-of-the-arts.

Motivated by a number of security applications, among which border patrolling, we study, to the best of our knowledge, the first Security Game model in which patrolling strategies need to be combined with responses to signals raised by an alarm system, which is spatially uncertain (i.e., it is uncertain over the exact location the attack is ongoing) and is affected by false negatives (i.e., the missed detection rate of an attack may be positive). Ours is an infinite-horizon patrolling scenario on a graph, where a single patroller moves. We study the properties of the game model in terms of computational issues and form of the optimal strategies and we provide an approach to solve it. Finally, we provide an experimental analysis of our techniques.

In this paper we theoretically study the minimum Differentially Resolving Set (DRS) problem derived from the classical sensor placement optimization problem in network source locating. A DRS of a graph G = ( V, E ) is defined as a subset S ⊆ V where any two elements in V can be distinguished by their different differential characteristic sets defined on S. The minimum DRS problem aims to find a DRS S in the graph G with minimum total weight Σ v∈S w ( v ). In this paper we establish a group of Integer Linear Programming (ILP) models as the solution. By the weighted set cover theory, we propose an approximation algorithm with the Θ(ln n ) approximability for the minimum DRS problem on general graphs, where n is the graph size.

Kidney exchange is a type of barter market where patients exchange willing but incompatible donors. These exchanges are conducted via cycles---where each incompatible patient-donor pair in the cycle both gives and receives a kidney---and chains, which are started by an altruist donor who does not need a kidney in return. Finding the best combination of cycles and chains is hard. The leading algorithms for this optimization problem use either branch and price — a combination of branch and bound and column generation — or constraint generation. We show a correctness error in the leading prior branch-and-price-based approach [Glorie et al. 2014]. We develop a provably correct fix to it, which also necessarily changes the algorithm's complexity, as well as other improvements to the search algorithm. Next, we compare our solver to the leading constraint-generation-based solver and to the best prior correct branch-and-price-based solver. We focus on the setting where chains have a length cap. A cap is desirable in practice since if even one edge in the chain fails, the rest of the chain fails: the cap precludes very long chains that are extremely unlikely to execute and instead causes the solution to have more parallel chains and cycles that are more likely to succeed. We work with the UNOS nationwide kidney exchange, which uses a chain cap. Algorithms from our group autonomously make the transplant plans for that exchange. On that real data and demographically-accurate generated data, our new solver scales significantly better than the prior leading approaches.

Policy Iteration (PI) (Howard 1960) is a classical method for computing an optimal policy for a finite Markov Decision Problem (MDP). The method is conceptually simple: starting from some initial policy, “policy improvement” is repeatedly performed to obtain progressively dominating policies, until eventually, an optimal policy is reached. Being remarkably efficient in practice, PI is often favoured over alternative approaches such as Value Iteration and Linear Programming. Unfortunately, even after several decades of study, theoretical bounds on the complexity of PI remain unsatisfactory. For an MDP with n states and k actions, Mansour and Singh (1999) bound the number of iterations taken by Howard’s PI, the canonical variant of the method, by O ( k n / n ). This bound merely improves upon the trivial bound of kn by a linear factor. However, a randomised variant of PI introduced by Mansour and Singh (1999) does yield an exponential improvement, with its expected number of iterations bounded by O(((1 + 2/log 2 ( k )) k / 2) n ).With the objective of furnishing improved upper bounds for PI, we introduce two randomised procedures in this paper. Our first contribution is a routine to find a good initial policy for PI. After evaluating a number of randomly generated policies, this procedure applies a novel criterion to pick one to initialise PI. When PI is subsequently applied, we show that the expected number of policy evaluations—including both the initialisation and the improvement stages—remains bounded in expectation by O ( k n /2 ). The key construction employed in this routine is a total order on the set of policies. Our second contribution is a randomised action-switching rule for PI, which admits a bound of O((2 + ln( k – 1)) n ) on the expected number of iterations. To the best of our knowledge, this is the tightest complexity bound known for PI when k >= 3.  

The leading approach to solving large imperfect information games is to pre-calculate an approximate solution using a simplified abstraction of the full game; that solution is then used to play the original, full-scale game. The abstraction step is necessitated by the size of the game tree. However, as the original game progresses, the remaining portion of the tree (the subgame) becomes smaller. An appealing idea is to use the simplified abstraction to play the early parts of the game and then, once the subgame becomes tractable, to calculate a solution using a finer-grained abstraction in real time, creating a combined final strategy. While this approach is straightforward for perfect information games, it is a much more complex problem for imperfect information games. If the subgame is solved locally, the opponent can alter his play in prior to this subgame to exploit our combined strategy. To prevent this, we introduce the notion of subgame margin, a simple value with appealing properties. If any best response reaches the subgame, the improvement of exploitability of the combined strategy is (at least) proportional to the subgame margin. This motivates subgame refinements resulting in large positive margins. Unfortunately, current techniques either neglect subgame margin (potentially leading to a large negative subgame margin and drastically more exploitable strategies), or guarantee only non-negative subgame margin (possibly producing the original, unrefined strategy, even if much stronger strategies are possible). Our technique remedies this problem by maximizing the subgame margin and is guaranteed to find the optimal solution. We evaluate our technique using one of the top participants of the AAAI-14 Computer Poker Competition, the leading playground for agents in imperfect information setting

Resource optimization and scheduling is a costly, challenging problem that affects almost every aspect of our lives. One example that affects each of us is health care: Poor systems design and scheduling of resources can lead to higher rates of patient noncompliance and burnout of health care providers, as highlighted by the Institute of Medicine (Brandenburg et al. 2015). In aerospace manufacturing, every minute re-scheduling in response to dynamic disruptions in the build process of a Boeing 747 can cost up to $100.000. The military is also highly invested in the effective use of resources. In missile defense, for example, operators must =solve a challenging weapon-to-target problem, balancing the cost of expendable, defensive weapons while hedging against uncertainty in adversaries’ tactics. Researchers in artificial intelligence (AI) planning and scheduling strive to develop algorithms to improve resource allocation. However, there are two primary challenges. First, optimal task allocation and sequencing with upper and lower-bound temporal constraints (i.e., deadlines and wait constraints) is NP-Hard (Bertsimas and Weismantel 2005). Approximation techniques for scheduling exist and typically rely on the algorithm designer crafting heuristics based on domain expertise to decompose or structure the scheduling problem and prioritize the manner in which resources are allocated and tasks are sequenced (Tang and Parker 2005; Jones, Dias, and Stentz 2011). The second problem is this aforementioned reliance on crafting clever heuristics based on domain knowledge. Manually capturing domain knowledge within a scheduling algorithm remains a challenging process and leaves much to be desired (Ryan et al. 2013). The aim of my thesis is to develop an autonomous system that 1) learns the heuristics and implicit rules-of-thumb developed by domain experts from years of experience, 2) embeds and leverages this knowledge within a scalable resource optimization framework, and 3) provides decision support in a way that engages users and benefits them in their decision-making process. By intelligently leveraging the ability of humans to learn heuristics and the speed of modern computation, we can improve the ability to coordinate resources in these time and safety-critical domains.

This paper considers prescriptive evacuation planning for a region threatened by a natural disaster such a flood, a wildfire, or a hurricane. It proposes a Benders decomposition that generalizes the two-stage approach proposed in earlier work for convergent evacuation plans. Experimental results show that Benders decomposition provides significant improvements in solution quality in reasonable time: It finds provably optimal solutions to scenarios considered in prior work, closing these instances, and increases the number of evacuees by 10 to 15% on average on more complex flood scenarios.