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Algorithms Behind Modern Storage Systems
Developing storage systems always presents the same challenges and factors to consider. Deciding what to optimize for has a substantial influence on the result. You can spend more time during write in order to lay out structures for more efficient reads, reserve extra space for in-place updates, facilitate faster writes, and buffer data in memory to ensure sequential write operations. It is impossible, however, to do this all at once. An ideal storage system would have the lowest read cost, lowest write cost, and no overhead.
Learning Heuristics for Automated Reasoning through Deep Reinforcement Learning
Lederman, Gil, Rabe, Markus N., Seshia, Sanjit A.
We demonstrate how to learn efficient heuristics for automated reasoning algorithms through deep reinforcement learning. We consider search algorithms for quantified Boolean logics, that already can solve formulas of impressive size - up to 100s of thousands of variables. The main challenge is to find a representation which lends to making predictions in a scalable way. The heuristics learned through our approach significantly improve over the handwritten heuristics for several sets of formulas.
Multitask Reinforcement Learning for Zero-shot Generalization with Subtask Dependencies
Sohn, Sungryull, Oh, Junhyuk, Lee, Honglak
We introduce a new RL problem where the agent is required to execute a given subtask graph which describes a set of subtasks and their dependency. Unlike existing multitask RL approaches that explicitly describe what the agent should do, a subtask graph in our problem only describes properties of subtasks and relationships among them, which requires the agent to perform complex reasoning to find the optimal sequence of subtasks to execute. To tackle this problem, we propose a neural subtask graph solver (NSS) which encodes the subtask graph using a recursive neural network. To overcome the difficulty of training, we propose a novel non-parametric gradient-based policy to pre-train our NSS agent. % and further finetune it through actor-critic method. The experimental results on two 2D visual domains show that our agent can perform complex reasoning to find a near-optimal way of executing the subtask graph and generalize well to the unseen subtask graphs. In addition, we compare our agent with a Monte-Carlo tree search (MCTS) method showing that (1) our method is much more efficient than MCTS and (2) combining MCTS with NSS dramatically improves the search performance.
Preference-Based Monte Carlo Tree Search
Joppen, Tobias, Wirth, Christian, Fรผrnkranz, Johannes
Monte Carlo tree search (MCTS) is a popular choice for solving sequential anytime problems. However, it depends on a numeric feedback signal, which can be difficult to define. Real-time MCTS is a variant which may only rarely encounter states with an explicit, extrinsic reward. To deal with such cases, the experimenter has to supply an additional numeric feedback signal in the form of a heuristic, which intrinsically guides the agent. Recent work has shown evidence that in different areas the underlying structure is ordinal and not numerical. Hence erroneous and biased heuristics are inevitable, especially in such domains. In this paper, we propose a MCTS variant which only depends on qualitative feedback, and therefore opens up new applications for MCTS. We also find indications that translating absolute into ordinal feedback may be beneficial. Using a puzzle domain, we show that our preference-based MCTS variant, wich only receives qualitative feedback, is able to reach a performance level comparable to a regular MCTS baseline, which obtains quantitative feedback.
Monte Carlo Methods for the Game Kingdomino
Gedda, Magnus, Lagerkvist, Mikael Z., Butler, Martin
Kingdomino is introduced as an interesting game for studying game playing: the game is multiplayer (4 independent players per game); it has a limited game depth (13 moves per player); and it has limited but not insignificant interaction among players. Several strategies based on locally greedy players, Monte Carlo Evaluation (MCE), and Monte Carlo Tree Search (MCTS) are presented with variants. We examine a variation of UCT called progressive win bias and a playout policy (Player-greedy) focused on selecting good moves for the player. A thorough evaluation is done showing how the strategies perform and how to choose parameters given specific time constraints. The evaluation shows that surprisingly MCE is stronger than MCTS for a game like Kingdomino. All experiments use a cloud-native design, with a game server in a Docker container, and agents communicating using a REST-style JSON protocol. This enables a multi-language approach to separating the game state, the strategy implementations, and the coordination layer.
Exponential Weights on the Hypercube in Polynomial Time
We study a general online linear optimization problem(OLO). At each round, a subset of objects from a fixed universe of $n$ objects is chosen, and a linear cost associated with the chosen subset is incurred. We use \textit{regret} as a measure of performance of our algorithms. Regret is the difference between the total cost incurred over all iterations and the cost of the best fixed subset in hindsight. We consider \textit{Full Information}, \textit{Semi-Bandit} and \textit{Bandit} feedback for this problem. Using characteristic vectors of the subsets, this problem reduces to OLO on the $\{0,1\}^n$ hypercube. The Exp2 algorithm and its bandit variants are commonly used strategies for this problem. It was previously unknown if it is possible to run Exp2 on the hypercube in polynomial time. In this paper, we present a polynomial time algorithm called \textit{PolyExp} for OLO on the hypercube. We show that our algorithm is equivalent to both Exp2 on $\{0,1\}^n$ as well as Online Mirror Descent(OMD) with Entropic regularization on $[0,1]^n$ and Bernoulli Sampling. Under $L_\infty$ adversarial losses, in the Full Information case and Semi-Bandit case, analyzing Exp2 directly, gives an expected regret bound of $O(n^{3/2}\sqrt{T})$, whereas PolyExp yields a regret of $O(n\sqrt{T})$. In the Bandit case, analyzing Exp2 directly, gives an expected regret bound of $O(n^{2}\sqrt{T})$, whereas PolyExp yields a regret of $O(n^{3/2}\sqrt{T})$. This implies an improvement on Exp2's regret bound for these settings because of the equivalence. Moreover, PolyExp is minimax optimal in all the three settings as its regret bounds match the $L_\infty$ lowerbounds in \cite{audibert2011minimax}. Finally, we show how to use PolyExp on the $\{-1,+1\}^n$ hypercube, solving an open problem in \cite{bubeck2012towards}.
A survey on policy search algorithms for learning robot controllers in a handful of trials
Chatzilygeroudis, Konstantinos, Vassiliades, Vassilis, Stulp, Freek, Calinon, Sylvain, Mouret, Jean-Baptiste
Most policy search algorithms require thousands of training episodes to find an effective policy, which is often infeasible with a physical robot. This survey article focuses on the extreme other end of the spectrum: how can a robot adapt with only a handful of trials (a dozen) and a few minutes? By analogy with the word "big-data", we refer to this challenge as "micro-data reinforcement learning". We show that a first strategy is to leverage prior knowledge on the policy structure (e.g., dynamic movement primitives), on the policy parameters (e.g., demonstrations), or on the dynamics (e.g., simulators). A second strategy is to create data-driven surrogate models of the expected reward (e.g., Bayesian optimization) or the dynamical model (e.g., model-based policy search), so that the policy optimizer queries the model instead of the real system. Overall, all successful micro-data algorithms combine these two strategies by varying the kind of model and prior knowledge. The current scientific challenges essentially revolve around scaling up to complex robots (e.g., humanoids), designing generic priors, and optimizing the computing time.
A Game-Based Approximate Verification of Deep Neural Networks with Provable Guarantees
Wu, Min, Wicker, Matthew, Ruan, Wenjie, Huang, Xiaowei, Kwiatkowska, Marta
Despite the improved accuracy of deep neural networks, the discovery of adversarial examples has raised serious safety concerns. In this paper, we study two variants of pointwise robustness, the maximum safe radius problem, which for a given input sample computes the minimum distance to an adversarial example, and the feature robustness problem, which aims to quantify the robustness of individual features to adversarial perturbations. We demonstrate that, under the assumption of Lipschitz continuity, both problems can be approximated using finite optimisation by discretising the input space, and the approximation has provable guarantees, i.e., the error is bounded. We then show that the resulting optimisation problems can be reduced to the solution of two-player turn-based games, where the first player selects features and the second perturbs the image within the feature. While the second player aims to minimise the distance to an adversarial example, depending on the optimisation objective the first player can be cooperative or competitive. We employ an anytime approach to solve the games, in the sense of approximating the value of a game by monotonically improving its upper and lower bounds. The Monte Carlo tree search algorithm is applied to compute upper bounds for both games, and the Admissible A* and the Alpha-Beta Pruning algorithms are, respectively, used to compute lower bounds for the maximum safety radius and feature robustness games. When working on the upper bound of the maximum safe radius problem, our tool demonstrates competitive performance against existing adversarial example crafting algorithms. Furthermore, we show how our framework can be deployed to evaluate pointwise robustness of neural networks in safety-critical applications such as traffic sign recognition in self-driving cars.
Ranked Reward: Enabling Self-Play Reinforcement Learning for Combinatorial Optimization
Laterre, Alexandre, Fu, Yunguan, Jabri, Mohamed Khalil, Cohen, Alain-Sam, Kas, David, Hajjar, Karl, Dahl, Torbjorn S., Kerkeni, Amine, Beguir, Karim
Adversarial self-play in two-player games has delivered impressive results when used with reinforcement learning algorithms that combine deep neural networks and tree search. Algorithms like AlphaZero and Expert Iteration learn tabula-rasa, producing highly informative training data on the fly. However, the self-play training strategy is not directly applicable to single-player games. Recently, several practically important combinatorial optimization problems, such as the traveling salesman problem and the bin packing problem, have been reformulated as reinforcement learning problems, increasing the importance of enabling the benefits of self-play beyond two-player games. We present the Ranked Reward (R2) algorithm which accomplishes this by ranking the rewards obtained by a single agent over multiple games to create a relative performance metric. Results from applying the R2 algorithm to instances of a two-dimensional bin packing problem show that it outperforms generic Monte Carlo tree search, heuristic algorithms and reinforcement learning algorithms not using ranked rewards.