Is there a predefined variable for "/home/vsts" in Azure Pipelines?

No, there is no such variable. You can use one of the /home/vsts/work paths and cache $(System.WorkFolder)/../.cache/torch/.

Values of predefined variables for an Ubuntu agent:

Agent.AcceptTeeEula             True              
Agent.BuildDirectory            /home/vsts/work/1               
Agent.HomeDirectory             /home/vsts/agents/2.181.2              
Agent.Id                        32   
Agent.JobName                   Job        
Agent.JobStatus                 Succeeded          
Agent.MachineName               fv-az160-540            
Agent.Name                      Azure Pipelines 2     
Agent.OS                        Linux   
Agent.OSArchitecture            X64               
Agent.RetainDefaultEncoding     false                      
Agent.ReadOnlyVariables         true                  
Agent.RootDirectory             /home/vsts/work              
Agent.TempDirectory             /home/vsts/work/_temp              
Agent.ToolsDirectory            /opt/hostedtoolcache               
Agent.Version                   2.181.2        
Agent.WorkFolder                /home/vsts/work           
Build.ArtifactStagingDirectory  /home/vsts/work/1/a                         
Build.BinariesDirectory         /home/vsts/work/1/b                  
Build.DefinitionName            FooBar
Build.SourceBranch              refs/heads/FOOBAR-123-caching
Build.SourceVersion             2b2c45223722fc7226eb23d752fc722bcdee2c54
Build.SourcesDirectory          /home/vsts/work/1/s                 
Build.StagingDirectory          /home/vsts/work/1/a                 
Common.TestResultsDirectory     /home/vsts/work/1/TestResults                      
Pipeline.Workspace              /home/vsts/work/1             
System.AccessToken              ***             
System.ArtifactsDirectory       /home/vsts/work/1/a                    
System.CollectionId             c02d3c7b-9d74-4532-aa21-abccdf07c888
System.Culture                  en-US         
System.DefaultWorkingDirectory  /home/vsts/work/1/s                         
System.DefinitionId             26              
System.EnableAccessToken        SecretVariable                   
System.HostType                 build          
System.JobAttempt               1            
System.JobId                    33f11733-54f2-5aa3-20dd-22fc7dcf5912
System.JobName                  __default         
System.PhaseAttempt             1              
System.PhaseDisplayName         Job                  
System.PhaseName                Job           
System.ServerType               Hosted            
System.StageAttempt             1              
System.StageName                __default           
System.TeamProject              Foo Bar
System.TeamProjectId            3337a4f6-1411-40aa-beeb-0c7d86b9ecba
System.WorkFolder               /home/vsts/work            
Task.DisplayName                print predefined variables

If by "Predefined variables" you mean one of the variables specified in the documentation then no.

However if you are using Hosted Linux Agents you can simply look at the environment variable $HOME, which works at least if you are in a script:, which may or may not fit your use case.

Example:

trigger:
- main

pool:
  vmImage: ubuntu-latest

steps:
  - script: echo $HOME

The output of the script task is /home/vsts