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Petr Novotný

Publications and source records attributed to Petr Novotný.

At least 19 recordsLinked to original sources

Momba: Network Modernization Improves Multi-Objective Reinforcement Learning

Recent advances in deep reinforcement learning (RL) have shown that improving neural network architectures can yield substantial gains in sample efficiency and asymptotic performance without altering the underlying algorithms. In contrast, work on multi-objective reinforcement learning (MORL), which aims to discover a set of policies that balance trade-offs among conflicting objectives, has predominantly focused on algorithmic innovations, leaving the area of architectures underexplored. While the optimal policies and value functions can differ significantly depending on the trade-offs, MORL algorithms commonly represent them with simple feedforward networks conditioned on the trade-off. This raises the question of whether the performance of the algorithms could be improved with more expressive function approximators. In this paper, we integrate recent advances in neural network design: (i) observation and feature normalization, (ii) weight normalization, and (iii) modeling of distributional returns with an entropy-regularized MORL algorithm. The empirical results across standard continuous control benchmarks demonstrate that these changes substantially improve the quality of the produced solution sets without requiring major changes to the underlying algorithm.

cs.LG

Eight-dimensional Manin triples, Yang-Baxter deformations and solutions of Supergravity Equations

Extensive list of 4+4-dimensional Manin triples that was presented recently can be used to find new solutions of supergravity equations via Poisson-Lie T-plurality. To get the solutions we start with 1+3-dimensional flat backgrounds on Poisson-Lie groups corresponding to semi-Abelian Manin triples. For application of the Poisson-Lie T-plurality we identify Manin triples that form various decompositions of the same Drinfeld double. Beside flat backgrounds and plane-parallel waves solving supergravity equations, plurality transformation also produces curved backgrounds with torsion satisfying (generalized) supergravity equations. Many of the Poisson-Lie transformations can be understood as homogeneous Yang-Baxter deformations. Of special interest are the non-unimodular deformations leading to solutions of generalized supergravity equations.

hep-th

Classification of standard Manin triples in dimension 4+4

Four- and six-dimensional Drinfeld doubles were classified in the past in terms of Manin triples. We provide an important step towards the classification of eight-dimensional Drinfeld doubles by presenting an extensive list of Manin triples formed by pairs of four-dimensional Lie algebras. Due to the high complexity of the classification we focus on Manin triples formed by algebras in a certain standard form. The list contains 188 non-isomorphic Manin triples plus their duals. To apply the results, we construct several four-dimensional WZW models on non-semisimple Lie groups. Some of the WZW models are known from the literature, but new cases are presented as well. As a consequence of the construction method, the WZW models are Poisson--Lie dualizable.

hep-th

Games on Graphs: From Logic and Automata to Algorithms

The objective of this book is to give a comprehensive presentation of the research field concerned with infinite duration games on graphs. Historically, these game models appeared in the study of automata and logic, and they later became important for program verification and synthesis. They have many more applications, in particular some of the models investigated in this book were introduced and studied in neighbouring research communities such as optimisation, reinforcement learning, model theory, and set theory.

cs.GT

Taming Infinity one Chunk at a Time: Concisely Represented Strategies in One-Counter MDPs

Markov decision processes (MDPs) are a canonical model to reason about decision making within a stochastic environment. We study a fundamental class of infinite MDPs: one-counter MDPs (OC-MDPs). They extend finite MDPs via an associated counter taking natural values, thus inducing an infinite MDP over the set of configurations (current state and counter value). We consider two characteristic objectives: reaching a target state (state-reachability), and reaching a target state with counter value zero (selective termination). The synthesis problem for the latter is not known to be decidable and connected to major open problems in number theory. Furthermore, even seemingly simple strategies (e.g., memoryless ones) in OC-MDPs might be impossible to build in practice (due to the underlying infinite configuration space): we need finite, and preferably small, representations. To overcome these obstacles, we introduce two natural classes of concisely represented strategies based on a (possibly infinite) partition of counter values in intervals. For both classes, and both objectives, we study the verification problem (does a given strategy ensure a high enough probability for the objective?), and two synthesis problems (does there exist such a strategy?): one where the interval partition is fixed as input, and one where it is only parameterized. We develop a generic approach based on a compression of the induced infinite MDP that yields decidability in all cases, with all complexities within PSPACE.

cs.GT

Refuting Equivalence in Probabilistic Programs with Conditioning

We consider the problem of refuting equivalence of probabilistic programs, i.e., the problem of proving that two probabilistic programs induce different output distributions. We study this problem in the context of programs with conditioning (i.e., with observe and score statements), where the output distribution is conditioned by the event that all the observe statements along a run evaluate to true, and where the probability densities of different runs may be updated via the score statements. Building on a recent work on programs without conditioning, we present a new equivalence refutation method for programs with conditioning. Our method is based on weighted restarting, a novel transformation of probabilistic programs with conditioning to the output equivalent probabilistic programs without conditioning that we introduce in this work. Our method is the first to be both a) fully automated, and b) providing provably correct answers. We demonstrate the applicability of our method on a set of programs from the probabilistic inference literature.

cs.PL

Bidding Games on Markov Decision Processes with Quantitative Reachability Objectives

Graph games are fundamental in strategic reasoning of multi-agent systems and their environments. We study a new family of graph games which combine stochastic environmental uncertainties and auction-based interactions among the agents, formalized as bidding games on (finite) Markov decision processes (MDP). Normally, on MDPs, a single decision-maker chooses a sequence of actions, producing a probability distribution over infinite paths. In bidding games on MDPs, two players -- called the reachability and safety players -- bid for the privilege of choosing the next action at each step. The reachability player's goal is to maximize the probability of reaching a target vertex, whereas the safety player's goal is to minimize it. These games generalize traditional bidding games on graphs, and the existing analysis techniques do not extend. For instance, the central property of traditional bidding games is the existence of a threshold budget, which is a necessary and sufficient budget to guarantee winning for the reachability player. For MDPs, the threshold becomes a relation between the budgets and probabilities of reaching the target. We devise value-iteration algorithms that approximate thresholds and optimal policies for general MDPs, and compute the exact solutions for acyclic MDPs, and show that finding thresholds is at least as hard as solving simple-stochastic games.

cs.GT

Threshold UCT: Cost-Constrained Monte Carlo Tree Search with Pareto Curves

Constrained Markov decision processes (CMDPs), in which the agent optimizes expected payoffs while keeping the expected cost below a given threshold, are the leading framework for safe sequential decision making under stochastic uncertainty. Among algorithms for planning and learning in CMDPs, methods based on Monte Carlo tree search (MCTS) have particular importance due to their efficiency and extendibility to more complex frameworks (such as partially observable settings and games). However, current MCTS-based methods for CMDPs either struggle with finding safe (i.e., constraint-satisfying) policies, or are too conservative and do not find valuable policies. We introduce Threshold UCT (T-UCT), an online MCTS-based algorithm for CMDP planning. Unlike previous MCTS-based CMDP planners, T-UCT explicitly estimates Pareto curves of cost-utility trade-offs throughout the search tree, using these together with a novel action selection and threshold update rules to seek safe and valuable policies. Our experiments demonstrate that our approach significantly outperforms state-of-the-art methods from the literature.

cs.AI

Solving Long-run Average Reward Robust MDPs via Stochastic Games

Markov decision processes (MDPs) provide a standard framework for sequential decision making under uncertainty. However, MDPs do not take uncertainty in transition probabilities into account. Robust Markov decision processes (RMDPs) address this shortcoming of MDPs by assigning to each transition an uncertainty set rather than a single probability value. In this work, we consider polytopic RMDPs in which all uncertainty sets are polytopes and study the problem of solving long-run average reward polytopic RMDPs. We present a novel perspective on this problem and show that it can be reduced to solving long-run average reward turn-based stochastic games with finite state and action spaces. This reduction allows us to derive several important consequences that were hitherto not known to hold for polytopic RMDPs. First, we derive new computational complexity bounds for solving long-run average reward polytopic RMDPs, showing for the first time that the threshold decision problem for them is in $NP \cap coNP$ and that they admit a randomized algorithm with sub-exponential expected runtime. Second, we present Robust Polytopic Policy Iteration (RPPI), a novel policy iteration algorithm for solving long-run average reward polytopic RMDPs. Our experimental evaluation shows that RPPI is much more efficient in solving long-run average reward polytopic RMDPs compared to state-of-the-art methods based on value iteration.

cs.AI

Equivalence and Similarity Refutation for Probabilistic Programs

We consider the problems of statically refuting equivalence and similarity of output distributions defined by a pair of probabilistic programs. Equivalence and similarity are two fundamental relational properties of probabilistic programs that are essential for their correctness both in implementation and in compilation. In this work, we present a new method for static equivalence and similarity refutation. Our method refutes equivalence and similarity by computing a function over program outputs whose expected value with respect to the output distributions of two programs is different. The function is computed simultaneously with an upper expectation supermartingale and a lower expectation submartingale for the two programs, which we show to together provide a formal certificate for refuting equivalence and similarity. To the best of our knowledge, our method is the first approach to relational program analysis to offer the combination of the following desirable features: (1) it is fully automated, (2) it is applicable to infinite-state probabilistic programs, and (3) it provides formal guarantees on the correctness of its results. We implement a prototype of our method and our experiments demonstrate the effectiveness of our method to refute equivalence and similarity for a number of examples collected from the literature.

cs.PL

Synthesizing Resilient Strategies for Infinite-Horizon Objectives in Multi-Agent Systems

We consider the problem of synthesizing resilient and stochastically stable strategies for systems of cooperating agents striving to minimize the expected time between consecutive visits to selected locations in a known environment. A strategy profile is resilient if it retains its functionality even if some of the agents fail, and stochastically stable if the visiting time variance is small. We design a novel specification language for objectives involving resilience and stochastic stability, and we show how to efficiently compute strategy profiles (for both autonomous and coordinated agents) optimizing these objectives. Our experiments show that our strategy synthesis algorithm can construct highly non-trivial and efficient strategy profiles for environments with general topology.

cs.MA

Shielding in Resource-Constrained Goal POMDPs

We consider partially observable Markov decision processes (POMDPs) modeling an agent that needs a supply of a certain resource (e.g., electricity stored in batteries) to operate correctly. The resource is consumed by agent's actions and can be replenished only in certain states. The agent aims to minimize the expected cost of reaching some goal while preventing resource exhaustion, a problem we call \emph{resource-constrained goal optimization} (RSGO). We take a two-step approach to the RSGO problem. First, using formal methods techniques, we design an algorithm computing a \emph{shield} for a given scenario: a procedure that observes the agent and prevents it from using actions that might eventually lead to resource exhaustion. Second, we augment the POMCP heuristic search algorithm for POMDP planning with our shields to obtain an algorithm solving the RSGO problem. We implement our algorithm and present experiments showing its applicability to benchmarks from the literature.

cs.AI

On-the-fly Adaptation of Patrolling Strategies in Changing Environments

We consider the problem of efficient patrolling strategy adaptation in a changing environment where the topology of Defender's moves and the importance of guarded targets change unpredictably. The Defender must instantly switch to a new strategy optimized for the new environment, not disrupting the ongoing patrolling task, and the new strategy must be computed promptly under all circumstances. Since strategy switching may cause unintended security risks compromising the achieved protection, our solution includes mechanisms for detecting and mitigating this problem. The efficiency of our framework is evaluated experimentally.

cs.MA

Proving Almost-Sure Termination of Probabilistic Programs via Incremental Pruning

The extension of classical imperative programs with real-valued random variables and random branching gives rise to probabilistic programs. The termination problem is one of the most fundamental liveness properties for such programs. The qualitative (aka almost-sure) termination problem asks whether a given program terminates with probability 1. Ranking functions provide a sound and complete approach for termination of non-probabilistic programs, and their extension to probabilistic programs is achieved via ranking supermartingales (RSMs). RSMs have been extended to lexicographic RSMs to handle programs with involved control-flow structure, as well as for compositional approach. There are two key limitations of the existing RSM-based approaches: First, the lexicographic RSM-based approach requires a strong nonnegativity assumption, which need not always be satisfied. The second key limitation of the existing RSM-based algorithmic approaches is that they rely on pre-computed invariants. The main drawback of relying on pre-computed invariants is the insufficiency-inefficiency trade-off: weak invariants might be insufficient for RSMs to prove termination, while using strong invariants leads to inefficiency in computing them. Our contributions are twofold: First, we show how to relax the strong nonnegativity condition and still provide soundness guarantee for almost-sure termination. Second, we present an incremental approach where the process of computing lexicographic RSMs proceeds by iterative pruning of parts of the program that were already shown to be terminating, in cooperation with a safety prover. In particular, our technique does not rely on strong pre-computed invariants. We present experimental results to show the applicability of our approach to examples of probabilistic programs from the literature.

cs.PL

On Lexicographic Proof Rules for Probabilistic Termination

We consider the almost-sure (a.s.) termination problem for probabilistic programs, which are a stochastic extension of classical imperative programs. Lexicographic ranking functions provide a sound and practical approach for termination of non-probabilistic programs, and their extension to probabilistic programs is achieved via lexicographic ranking supermartingales (LexRSMs). However, LexRSMs introduced in the previous work have a limitation that impedes their automation: all of their components have to be non-negative in all reachable states. This might result in LexRSM not existing even for simple terminating programs. Our contributions are twofold: First, we introduce a generalization of LexRSMs which allows for some components to be negative. This standard feature of non-probabilistic termination proofs was hitherto not known to be sound in the probabilistic setting, as the soundness proof requires a careful analysis of the underlying stochastic process. Second, we present polynomial-time algorithms using our generalized LexRSMs for proving a.s. termination in broad classes of linear-arithmetic programs.

cs.PL

Efficient Strategy Synthesis for MDPs with Resource Constraints

We consider qualitative strategy synthesis for the formalism called consumption Markov decision processes. This formalism can model dynamics of an agents that operates under resource constraints in a stochastic environment. The presented algorithms work in time polynomial with respect to the representation of the model and they synthesize strategies ensuring that a given set of goal states will be reached (once or infinitely many times) with probability 1 without resource exhaustion. In particular, when the amount of resource becomes too low to safely continue in the mission, the strategy changes course of the agent towards one of a designated set of reload states where the agent replenishes the resource to full capacity; with sufficient amount of resource, the agent attempts to fulfill the mission again. We also present two heuristics that attempt to reduce expected time that the agent needs to fulfill the given mission, a parameter important in practical planning. The presented algorithms were implemented and numerical examples demonstrate (i) the effectiveness (in terms of computation time) of the planning approach based on consumption Markov decision processes and (ii) the positive impact of the two heuristics on planning in a realistic example.

cs.AI

Proving Non-termination by Program Reversal

We present a new approach to proving non-termination of non-deterministic integer programs. Our technique is rather simple but efficient. It relies on a purely syntactic reversal of the program's transition system followed by a constraint-based invariant synthesis with constraints coming from both the original and the reversed transition system. The latter task is performed by a simple call to an off-the-shelf SMT-solver, which allows us to leverage the latest advances in SMT-solving. Moreover, our method offers a combination of features not present (as a whole) in previous approaches: it handles programs with non-determinism, provides relative completeness guarantees and supports programs with polynomial arithmetic. The experiments performed with our prototype tool RevTerm show that our approach, despite its simplicity and stronger theoretical guarantees, is at least on par with the state-of-the-art tools, often achieving a non-trivial improvement under a proper configuration of its parameters.

cs.PL

Qualitative Controller Synthesis for Consumption Markov Decision Processes

Consumption Markov Decision Processes (CMDPs) are probabilistic decision-making models of resource-constrained systems. In a CMDP, the controller possesses a certain amount of a critical resource, such as electric power. Each action of the controller can consume some amount of the resource. Resource replenishment is only possible in special reload states, in which the resource level can be reloaded up to the full capacity of the system. The task of the controller is to prevent resource exhaustion, i.e. ensure that the available amount of the resource stays non-negative, while ensuring an additional linear-time property. We study the complexity of strategy synthesis in consumption MDPs with almost-sure Büchi objectives. We show that the problem can be solved in polynomial time. We implement our algorithm and show that it can efficiently solve CMDPs modelling real-world scenarios.

cs.FL